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Problem Set: Graphs

Practice Makes Perfect

Plot Points on a Rectangular Coordinate System In the following exercises, plot each point on a coordinate grid. [latex-display]\left(3,2\right)[/latex-display] [latex-display]\left(4,1\right)[/latex-display] [latex-display]\left(1,5\right)[/latex-display] [latex-display]\left(3,4\right)[/latex-display] [latex-display]\left(4,1\right),\left(1,4\right)[/latex-display] [latex-display]\left(3,2\right),\left(2,3\right)[/latex-display] [latex-display]\left(3,4\right),\left(4,3\right)[/latex-display] In the following exercises, plot each point on a coordinate grid and identify the quadrant in which the point is located. ⓐ $\left(-4,2\right)$ ⓑ $\left(-1,-2\right)$ ⓒ $\left(3,-5\right)$ ⓓ $\left(2,\Large\frac{5}{2}\normalsize\right)$ ⓐ $\left(-2,-3\right)$ ⓑ $\left(3,-3\right)$ ⓒ $\left(-4,1\right)$ ⓓ $\left(1,\Large\frac{3}{2}\normalsize\right)$ ⓐ $\left(-1,1\right)$ ⓑ $\left(-2,-1\right)$ ⓒ $\left(1,-4\right)$ ⓓ $\left(3,\Large\frac{7}{2}\normalsize\right)$ ⓐ $\left(3,-2\right)$ ⓑ $\left(-3,2\right)$ ⓒ $\left(-3,-2\right)$ ⓓ $\left(3,2\right)$ ⓐ $\left(4,-1\right)$ ⓑ $\left(-4,1\right)$ ⓒ $\left(-4,-1\right)$ ⓓ $\left(4,1\right)$ ⓐ $\left(-2,0\right)$ ⓑ $\left(-3,0\right)$ ⓒ $\left(0,4\right)$ ⓓ $\left(0,2\right)$ Identify Points on a Graph In the following exercises, name the ordered pair of each point shown. Verify Solutions to an Equation in Two Variables In the following exercises, determine which ordered pairs are solutions to the given equation. [latex-display]2x+y=6[/latex-display] ⓐ $\left(1,4\right)$ ⓑ $\left(3,0\right)$ ⓒ $\left(2,3\right)$ ⓐ, ⓑ [latex-display]x+3y=9[/latex-display]
1. ⓐ $\left(0,3\right)$
2. ⓑ $\left(6,1\right)$
3. ⓒ $\left(-3,-3\right)$
[latex-display]4x - 2y=8[/latex-display] ⓐ $\left(3,2\right)$ ⓑ $\left(1,4\right)$ ⓒ $\left(0,-4\right)$ ⓐ, ⓒ [latex-display]3x - 2y=12[/latex-display] ⓐ $\left(4,0\right)$ ⓑ $\left(2,-3\right)$ ⓒ $\left(1,6\right)$ [latex-display]y=4x+3[/latex-display] ⓐ $\left(4,3\right)$ ⓑ $\left(-1,-1\right)$ ⓒ $\left(\Large\frac{1}{2}\normalsize,5\right)$ ⓑ, ⓒ [latex-display]y=2x - 5[/latex-display] ⓐ $\left(0,-5\right)$ ⓑ $\left(2,1\right)$ ⓒ $\left(\Large\frac{1}{2}\normalsize ,-4\right)$ [latex-display]y=\Large\frac{1}{2}\normalsize x - 1[/latex-display] ⓐ $\left(2,0\right)$ ⓑ $\left(-6,-4\right)$ ⓒ $\left(-4,-1\right)$ ⓐ, ⓑ [latex-display]y=\Large\frac{1}{3}\normalsize x+1[/latex-display] ⓐ $\left(-3,0\right)$ ⓑ $\left(9,4\right)$ ⓒ $\left(-6,-1\right)$ Find Solutions to Linear Equations in Two Variables In the following exercises, complete the table to find solutions to each linear equation. [latex-display]y=2x - 4[/latex-display]
$x$ $y$ $\left(x,y\right)$
$-1$
$0$
$2$
$x$ $y$ $\left(x,y\right)$
$-1$ $-6$ $\left(-1,-6\right)$
$0$ $-4$ $\left(0,-4\right)$
$2$ $0$ $\left(2,0\right)$
[latex-display]y=3x - 1[/latex-display]
$x$ $y$ $\left(x,y\right)$
$-1$
$0$
$2$
[latex-display]y=-x+5[/latex-display]
$x$ $y$ $\left(x,y\right)$
$-2$
$0$
$3$
$x$ $y$ $\left(x,y\right)$
$-2$ $7$ $\left(-2,7\right)$
$0$ $5$ $\left(0,5\right)$
$3$ $2$ $\left(3,2\right)$
[latex-display]y=\Large\frac{1}{3}\normalsize x+1[/latex-display]
$x$ $y$ $\left(x,y\right)$
$0$
$3$
$6$
[latex-display]y=-\Large\frac{3}{2}\normalsize x - 2[/latex-display]
$x$ $y$ $\left(x,y\right)$
$-2$
$0$
$2$
$x$ $y$ $\left(x,y\right)$
$-2$ $1$ $\left(-2,1\right)$
$0$ $-2$ $\left(0,-2\right)$
$2$ $-5$ $\left(2,-5\right)$
[latex-display]x+2y=8[/latex-display]
$x$ $y$ $\left(x,y\right)$
$0$
$4$
$0$

Everyday Math

Weight of a baby Mackenzie recorded her baby’s weight every two months. The baby’s age, in months, and weight, in pounds, are listed in the table, and shown as an ordered pair in the third column. ⓐ Plot the points on a coordinate grid.
 $\text{Age}$ $\text{Weight}$ $\left(x,y\right)$ $0$ $7$ $\left(0,7\right)$ $2$ $11$ $\left(2,11\right)$ $4$ $15$ $\left(4,15\right)$ $6$ $16$ $\left(6,16\right)$ $8$ $19$ $\left(8,19\right)$ $10$ $20$ $\left(10,20\right)$ $12$ $21$ $\left(12,21\right)$
ⓑ Why is only Quadrant I needed? ⓐ ⓑ Age and weight are only positive. Weight of a child Latresha recorded her son’s height and weight every year. His height, in inches, and weight, in pounds, are listed in the table, and shown as an ordered pair in the third column. ⓐ Plot the points on a coordinate grid.
 $\begin{array}{c}\text{Height}\hfill \\ x\hfill \end{array}$ $\begin{array}{c}\text{Weight}\hfill \\ y\hfill \end{array}$ $\begin{array}{}\\ \left(x,y\right)\hfill \end{array}$ $28$ $22$ $\left(28,22\right)$ $31$ $27$ $\left(31,27\right)$ $33$ $33$ $\left(33,33\right)$ $37$ $35$ $\left(37,35\right)$ $40$ $41$ $\left(40,41\right)$ $42$ $45$ $\left(42,45\right)$
ⓑ Why is only Quadrant I needed?

Writing Exercises

Have you ever used a map with a rectangular coordinate system? Describe the map and how you used it. Answers may vary. How do you determine if an ordered pair is a solution to a given equation?

Practice Makes Perfect

Identify the Intercepts on a Graph In the following exercises, find the $x\text{-}$ and $y\text{-}$ intercepts. (3,0),(0,3) (5,0),(0,−5) (−2,0),(0,−2) (−1,0),(0,1) (0,0) Find the $x$ and $y$ Intercepts from an Equation of a Line In the following exercises, find the intercepts. [latex-display]x+y=4[/latex-display] (4,0),(0,4) [latex-display]x+y=3[/latex-display] [latex-display]x+y=-2[/latex-display] (−2,0),(0,−2) [latex-display]x+y=-5[/latex-display] [latex-display]x-y=5[/latex-display] (5,0),(0,−5) [latex-display]x-y=1[/latex-display] [latex-display]x-y=-3[/latex-display] (−3,0),(0,3) [latex-display]x-y=-4[/latex-display] [latex-display]x+2y=8[/latex-display] (8,0),(0,4) [latex-display]x+2y=10[/latex-display] [latex-display]3x+y=6[/latex-display] (2,0),(0,6) [latex-display]3x+y=9[/latex-display] [latex-display]x - 3y=12[/latex-display] (12,0),(0,−4) [latex-display]x - 2y=8[/latex-display] [latex-display]4x-y=8[/latex-display] (2,0),(0,−8) [latex-display]5x-y=5[/latex-display] [latex-display]2x+5y=10[/latex-display] (5,0),(0,2) [latex-display]2x+3y=6[/latex-display] [latex-display]3x - 2y=12[/latex-display] (4,0),(0,−6) [latex-display]3x - 5y=30[/latex-display] [latex-display]y=\Large\frac{1}{3}\normalsize x - 1[/latex-display] (3,0),(0,−1) [latex-display]y=\Large\frac{1}{4}\normalsize x - 1[/latex-display] [latex-display]y=\Large\frac{1}{5}\normalsize x+2[/latex-display] (−10,0),(0,2) [latex-display]y=\Large\frac{1}{3}\normalsize x+4[/latex-display] [latex-display]y=3x[/latex-display] (0,0) [latex-display]y=-2x[/latex-display] [latex-display]y=-4x[/latex-display] (0,0) [latex-display]y=5x[/latex-display] Graph a Line Using the Intercepts In the following exercises, graph using the intercepts. [latex-display]-x+5y=10[/latex-display] [latex-display]-x+4y=8[/latex-display] [latex-display]x+2y=4[/latex-display] [latex-display]x+2y=6[/latex-display] [latex-display]x+y=2[/latex-display] [latex-display]x+y=5[/latex-display] [latex-display]x+y=-3[/latex-display] [latex-display]x+y=-1[/latex-display] [latex-display]x-y=1[/latex-display] [latex-display]x-y=2[/latex-display] [latex-display]x-y=-4[/latex-display] [latex-display]x-y=-3[/latex-display] [latex-display]4x+y=4[/latex-display] [latex-display]3x+y=3[/latex-display] [latex-display]3x-y=-6[/latex-display] [latex-display]2x-y=-8[/latex-display] [latex-display]2x+4y=12[/latex-display] [latex-display]3x+2y=12[/latex-display] [latex-display]3x - 2y=6[/latex-display] [latex-display]5x - 2y=10[/latex-display] [latex-display]2x - 5y=-20[/latex-display] [latex-display]3x - 4y=-12[/latex-display] [latex-display]y=-2x[/latex-display] [latex-display]y=-4x[/latex-display] [latex-display]y=x[/latex-display] [latex-display]y=3x[/latex-display] Choose the Most Convenient Method to Graph a Line In the following exercises, identify the most convenient method to graph each line. [latex-display]x=2[/latex-display] vertical line [latex-display]y=4[/latex-display] [latex-display]y=5[/latex-display] horizontal line [latex-display]x=-3[/latex-display] [latex-display]y=-3x+4[/latex-display] plotting points [latex-display]y=-5x+2[/latex-display] [latex-display]x-y=5[/latex-display] intercepts [latex-display]x-y=1[/latex-display] [latex-display]y=\Large\frac{2}{3}\normalsize x - 1[/latex-display] plotting points [latex-display]y=\Large\frac{4}{5}\normalsize x - 3[/latex-display] [latex-display]y=-3[/latex-display] horizontal line [latex-display]y=-1[/latex-display] [latex-display]3x - 2y=-12[/latex-display] intercepts [latex-display]2x - 5y=-10[/latex-display] [latex-display]y=-\Large\frac{1}{4}\normalsize x+3[/latex-display] plotting points [latex-display]y=-\Large\frac{1}{3}\normalsize x+5[/latex-display]

Everyday Math

Road trip Damien is driving from Chicago to Denver, a distance of $1,000$ miles. The $x\text{-axis}$ on the graph below shows the time in hours since Damien left Chicago. The $y\text{-axis}$ represents the distance he has left to drive. ⓐ Find the $x\text{-}$ and $y\text{-}$ intercepts ⓑ Explain what the $x\text{-}$ and $y\text{-}$ intercepts mean for Damien. ⓐ (0,1,000),(15,0). ⓑ At (0,1,000) he left Chicago 0 hours ago and has 1,000 miles left to drive. At (15,0) he left Chicago 15 hours ago and has 0 miles left to drive. Road trip Ozzie filled up the gas tank of his truck and went on a road trip. The $x\text{-axis}$ on the graph shows the number of miles Ozzie drove since filling up. The $y\text{-axis}$ represents the number of gallons of gas in the truck’s gas tank. ⓐ Find the $x\text{-}$ and $y\text{-}$ intercepts. ⓑ Explain what the $x\text{-}$ and $y\text{-}$ intercepts mean for Ozzie.

Writing Exercises

How do you find the $x\text{-intercept}$ of the graph of $3x - 2y=6?$ Answers will vary. How do you find the $y\text{-intercept}$ of the graph of $5x-y=10?$ Do you prefer to graph the equation $4x+y=-4$ by plotting points or intercepts? Why? Answers will vary. Do you prefer to graph the equation $y=\Large\frac{2}{3}\normalsize x - 2$ by plotting points or intercepts? Why?

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Practice Makes Perfect

Use Geoboards to Model Slope - CODE THESE in OHM In the following exercises, find the slope modeled on each geoboard. [latex-display]\Large\frac{1}{4}[/latex-display] [latex-display]-\Large\frac{3}{2}[/latex-display] In the following exercises, model each slope. Draw a picture to show your results. [latex-display]\Large\frac{2}{3}[/latex-display] [latex-display]\Large\frac{3}{4}[/latex-display] [latex-display]\Large\frac{1}{4}[/latex-display] [latex-display]\Large\frac{4}{3}[/latex-display] [latex-display]-\Large\frac{1}{2}[/latex-display] [latex-display]-\Large\frac{3}{4}[/latex-display] [latex-display]-\Large\frac{2}{3}[/latex-display] [latex-display]-\Large\frac{3}{2}[/latex-display] Find the Slope of a Line from its Graph In the following exercises, find the slope of each line shown. [latex-display]\Large\frac{2}{5}[/latex-display] [latex-display]\Large\frac{5}{4}[/latex-display] [latex-display]-\Large\frac{1}{3}[/latex-display] [latex-display]-\Large\frac{3}{4}[/latex-display] [latex-display]\Large\frac{3}{4}[/latex-display] [latex-display]-\Large\frac{5}{2}[/latex-display] [latex-display]-\Large\frac{2}{3}[/latex-display] [latex-display]\Large\frac{1}{4}[/latex-display] Find the Slope of Horizontal and Vertical Lines In the following exercises, find the slope of each line. [latex-display]y=3[/latex-display] 0 [latex-display]y=1[/latex-display] [latex-display]x=4[/latex-display] undefined [latex-display]x=2[/latex-display] [latex-display]y=-2[/latex-display] 0 [latex-display]y=-3[/latex-display] [latex-display]x=-5[/latex-display] undefined [latex-display]x=-4[/latex-display] Use the Slope Formula to find the Slope of a Line between Two Points In the following exercises, use the slope formula to find the slope of the line between each pair of points. [latex-display]\left(1,4\right),\left(3,9\right)[/latex-display] [latex-display]\Large\frac{5}{2}[/latex-display] [latex-display]\left(2,3\right),\left(5,7\right)[/latex-display] [latex-display]\left(0,3\right),\left(4,6\right)[/latex-display] [latex-display]\Large\frac{3}{4}[/latex-display] [latex-display]\left(0,1\right),\left(5,4\right)[/latex-display] [latex-display]\left(2,5\right),\left(4,0\right)[/latex-display] [latex-display]-\Large\frac{5}{2}[/latex-display] [latex-display]\left(3,6\right),\left(8,0\right)[/latex-display] [latex-display]\left(-3,3\right),\left(2,-5\right)[/latex-display] [latex-display]-\Large\frac{8}{5}[/latex-display] [latex-display]\left(-2,4\right),\left(3,-1\right)[/latex-display] [latex-display]\left(-1,-2\right),\left(2,5\right)[/latex-display] [latex-display]\Large\frac{7}{3}[/latex-display] [latex-display]\left(-2,-1\right),\left(6,5\right)[/latex-display] [latex-display]\left(4,-5\right),\left(1,-2\right)[/latex-display] −1 [latex-display]\left(3,-6\right),\left(2,-2\right)[/latex-display] Graph a Line Given a Point and the Slope In the following exercises, graph the line given a point and the slope. [latex-display]\left(1,-2\right);m=\Large\frac{3}{4}[/latex-display] [latex-display]\left(1,-1\right);m=\Large\frac{1}{2}[/latex-display] [latex-display]\left(2,5\right);m=-\Large\frac{1}{3}[/latex-display] [latex-display]\left(1,4\right);m=-\Large\frac{1}{2}[/latex-display] [latex-display]\left(-3,4\right);m=-\Large\frac{3}{2}[/latex-display] [latex-display]\left(-2,5\right);m=-\Large\frac{5}{4}[/latex-display] [latex-display]\left(-1,-4\right);m=\Large\frac{4}{3}[/latex-display] [latex-display]\left(-3,-5\right);m=\Large\frac{3}{2}[/latex-display] [latex-display]\left(0,3\right);m=-\Large\frac{2}{5}[/latex-display] [latex-display]\left(0,5\right);m=-\Large\frac{4}{3}[/latex-display] [latex-display]\left(-2,0\right);m=\Large\frac{3}{4}[/latex-display] [latex-display]\left(-1,0\right);m=\Large\frac{1}{5}[/latex-display] [latex-display]\left(-3,3\right);m=2[/latex-display] [latex-display]\left(-4,2\right);m=4[/latex-display] [latex-display]\left(1,5\right);m=-3[/latex-display] [latex-display]\left(2,3\right);m=-1[/latex-display] Solve Slope Applications In the following exercises, solve these slope applications. Slope of a roof A fairly easy way to determine the slope is to take a $\text{12-inch}$ level and set it on one end on the roof surface. Then take a tape measure or ruler, and measure from the other end of the level down to the roof surface. You can use these measurements to calculate the slope of the roof. What is the slope of the roof in this picture? [latex-display]\Large\frac{1}{3}[/latex-display] What is the slope of the roof shown? Road grade A local road has a grade of $\text{6%}$. The grade of a road is its slope expressed as a percent.
1. ⓐ Find the slope of the road as a fraction and then simplify the fraction.
2. ⓑ What rise and run would reflect this slope or grade?
ⓐ $\Large\frac{3}{50}$ ⓑ $\text{rise}=3;\text{run}=50$ Highway grade A local road rises $2$ feet for every $50$ feet of highway.
1. ⓐ What is the slope of the highway?
2. ⓑ The grade of a highway is its slope expressed as a percent. What is the grade of this highway?

Everyday Math

Wheelchair ramp The rules for wheelchair ramps require a maximum $1$ inch rise for a $12$ inch run.
1. ⓐ How long must the ramp be to accommodate a $\text{24-inch}$ rise to the door?
2. ⓑ Draw a model of this ramp.
ⓐ 288 inches (24 feet) ⓑ Models will vary. Wheelchair ramp A $\text{1-inch}$ rise for a $\text{16-inch}$ run makes it easier for the wheelchair rider to ascend the ramp.
1. ⓐ How long must the ramp be to easily accommodate a $\text{24-inch}$ rise to the door?
2. ⓑ Draw a model of this ramp.

Writing Exercises

What does the sign of the slope tell you about a line? Answers will vary. How does the graph of a line with slope $m=\Large\frac{1}{2}$ differ from the graph of a line with slope $m=2?$ Why is the slope of a vertical line undefined? Answers will vary. Explain how you can graph a line given a point and its slope.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Chapter Review Exercises

Use the Rectangular Coordinate System

Plot Points in a Rectangular Coordinate System In the following exercises, plot each point in a rectangular coordinate system. [latex-display]\left(1,3\right),\left(3,1\right)[/latex-display] [latex-display]\left(2,5\right),\left(5,2\right)[/latex-display] In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.
1. ⓐ $\left(-1,-5\right)$
2. ⓑ $\left(-3,4\right)$
3. ⓒ $\left(2,-3\right)$
4. ⓓ $\left(1,\Large\frac{5}{2}\normalsize\right)$
ⓐ III ⓑ II ⓒ IV ⓐ I
1. ⓐ $\left(3,-2\right)$
2. ⓑ $\left(-4,-1\right)$
3. ⓒ $\left(-5,4\right)$
4. ⓓ $\left(2,\Large\frac{10}{3}\normalsize\right)$
Identify Points on a Graph In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system. ⓐ (5,3) ⓑ (2,−1) ⓒ (−3,−2) ⓓ (−1,4) ⓐ (2,0) ⓑ (0,−5) ⓒ (−4,0) ⓓ (0,3) Verify Solutions to an Equation in Two Variables In the following exercises, find the ordered pairs that are solutions to the given equation. [latex-display]5x+y=10[/latex-display]
1. ⓐ $\left(5,1\right)$
2. ⓑ $\left(2,0\right)$
3. ⓒ $\left(4,-10\right)$
ⓑ,ⓒ [latex-display]y=6x - 2[/latex-display]
1. ⓐ $\left(1,4\right)$
2. ⓑ $\left(\Large\frac{1}{3}\normalsize ,0\right)$
3. ⓒ $\left(6,-2\right)$
Complete a Table of Solutions to a Linear Equation in Two Variables In the following exercises, complete the table to find solutions to each linear equation. [latex-display]y=4x - 1[/latex-display]
$x$ $y$ $\left(x,y\right)$
$0$
$1$
$-2$
$x$ $y$ $\left(x,y\right)$
$0$ $-1$ $\left(0,-1\right)$
$1$ $3$ $\left(1,3\right)$
$-2$ $-9$ $\left(-2,-9\right)$
[latex-display]y=-\Large\frac{1}{2}\normalsize x+3[/latex-display]
$x$ $y$ $\left(x,y\right)$
$0$
$1$
$-2$
[latex-display]x+2y=5[/latex-display]
$x$ $y$ $\left(x,y\right)$
$0$
$1$
$-1$
$x$ $y$ $\left(x,y\right)$
$5$ $0$ $\left(5,0\right)$
$1$ $2$ $\left(1,2\right)$
$-1$ $3$ $\left(-1,3\right)$
[latex-display]3x - 2y=6[/latex-display]
$x$ $y$ $\left(x,y\right)$
$0$
$0$
$-2$
Find Solutions to a Linear Equation in Two Variables In the following exercises, find three solutions to each linear equation. [latex-display]x+y=3[/latex-display] Answers will vary. [latex-display]x+y=-4[/latex-display] [latex-display]y=3x+1[/latex-display] Answers will vary. [latex-display]y=-x - 1[/latex-display]

Graphing Linear Equations

Recognize the Relation Between the Solutions of an Equation and its Graph In the following exercises, for each ordered pair, decide ⓐ if the ordered pair is a solution to the equation. ⓑ if the point is on the line. [latex-display]y=-x+4[/latex-display]
1. ⓐ $\left(0,4\right)$
2. ⓑ $\left(-1,3\right)$
3. ⓒ $\left(2,2\right)$
4. ⓓ $\left(-2,6\right)$
ⓐ yes ⓑ no ⓒ yes ⓓ yes ⓐ yes ⓑ no ⓒ yes ⓓ yes [latex-display]y=\Large\frac{2}{3}\normalsize x - 1[/latex-display]
1. ⓐ $\left(0,-1\right)$
2. ⓑ $\left(3,1\right)$
3. ⓒ $\left(-3,-3\right)$
4. ⓓ $\left(6,4\right)$
Graph a Linear Equation by Plotting Points In the following exercises, graph by plotting points. [latex-display]y=4x - 3[/latex-display] [latex-display]y=-3x[/latex-display] [latex-display]2x+y=7[/latex-display] Graph Vertical and Horizontal lines In the following exercises, graph the vertical or horizontal lines. [latex-display]y=-2[/latex-display] [latex-display]x=3[/latex-display]

Graphing with Intercepts

Identify the Intercepts on a Graph In the following exercises, find the $x\text{-}$ and $y\text{-intercepts}$. (0,3) (3,0) Find the Intercepts from an Equation of a Line In the following exercises, find the intercepts. [latex-display]x+y=5[/latex-display] [latex-display]x-y=-1[/latex-display] (−1,0) (0,1) [latex-display]y=\Large\frac{3}{4}\normalsize x - 12[/latex-display] [latex-display]y=3x[/latex-display] (0,0) Graph a Line Using the Intercepts In the following exercises, graph using the intercepts. [latex-display]-x+3y=3[/latex-display] [latex-display]x+y=-2[/latex-display] Choose the Most Convenient Method to Graph a Line In the following exercises, identify the most convenient method to graph each line. [latex-display]x=5[/latex-display] [latex-display]y=-3[/latex-display] horizontal line [latex-display]2x+y=5[/latex-display] [latex-display]x-y=2[/latex-display] intercepts [latex-display]y=\Large\frac{1}{2}\normalsize x+2[/latex-display] [latex-display]y=\Large\frac{3}{4}\normalsize x - 1[/latex-display] plotting points

Understand Slope of a Line

Use Geoboards to Model Slope In the following exercises, find the slope modeled on each geoboard. [latex-display]\Large\frac{4}{3}[/latex-display] [latex-display]-\Large\frac{2}{3}[/latex-display] In the following exercises, model each slope. Draw a picture to show your results. [latex-display]\Large\frac{1}{3}[/latex-display] [latex-display]\Large\frac{3}{2}[/latex-display] [latex-display]-\Large\frac{2}{3}[/latex-display] [latex-display]-\Large\frac{1}{2}[/latex-display] Find the Slope of a Line from its Graph In the following exercises, find the slope of each line shown. 1 [latex-display]-\Large\frac{1}{2}[/latex-display] Find the Slope of Horizontal and Vertical Lines In the following exercises, find the slope of each line. [latex-display]y=2[/latex-display] [latex-display]x=5[/latex-display] undefined [latex-display]x=-3[/latex-display] [latex-display]y=-1[/latex-display] 0 Use the Slope Formula to find the Slope of a Line between Two Points In the following exercises, use the slope formula to find the slope of the line between each pair of points. [latex-display]\left(2,1\right),\left(4,5\right)[/latex-display] [latex-display]\left(-1,-1\right),\left(0,-5\right)[/latex-display] −4 [latex-display]\left(3,5\right),\left(4,-1\right)[/latex-display] [latex-display]\left(-5,-2\right),\left(3,2\right)[/latex-display] [latex-display]\Large\frac{1}{2}[/latex-display] Graph a Line Given a Point and the Slope In the following exercises, graph the line given a point and the slope. [latex-display]\left(2,-2\right);m=\Large\frac{5}{2}[/latex-display] [latex-display]\left(-3,4\right);m=-\Large\frac{1}{3}[/latex-display] Solve Slope Applications In the following exercise, solve the slope application. A roof has rise $10$ feet and run $15$ feet. What is its slope?

Chapter Practice Test

Plot and label these points:
1. ⓐ $\left(2,5\right)$
2. ⓑ $\left(-1,-3\right)$
3. ⓒ $\left(-4,0\right)$
4. ⓓ $\left(3,-5\right)$
5. ⓔ $\left(-2,1\right)$
Name the ordered pair for each point shown. Find the $x\text{-intercept}$ and $y\text{-intercept}$ on the line shown. (4,0), (0,−2) Find the $x\text{-intercept}$ and $y\text{-intercept}$ of the equation $3x-y=6$. Is $\left(1,3\right)$ a solution to the equation $x+4y=12?$ How do you know? no; 1 + 4 · 3 ≠ 12 Complete the table to find four solutions to the equation $y=-x+1$.
 $x$ $y$ $\left(x,y\right)$ $0$ $1$ $3$ $-2$
Complete the table to find three solutions to the equation $4x+y=8$
 $x$ $y$ $\left(x,y\right)$ $0$ $0$ $3$
 $x$ $y$ $\left(x,y\right)$ $0$ $8$ $\left(0,8\right)$ $2$ $0$ $\left(2,0\right)$ $3$ $-4$ $\left(3,-4\right)$
In the following exercises, find three solutions to each equation and then graph each line. [latex-display]y=-3x[/latex-display] [latex-display]2x+3y=-6[/latex-display] In the following exercises, find the slope of each line. [latex-display]-\Large\frac{5}{2}[/latex-display] Use the slope formula to find the slope of the line between $\left(0,-4\right)$ and $\left(5,2\right)$. Find the slope of the line $y=2$. 0 Graph the line passing through $\left(1,1\right)$ with slope $m=\Large\frac{3}{2}$. A bicycle route climbs $20$ feet for $1,000$ feet of horizontal distance. What is the slope of the route? [latex-display]\Large\frac{1}{50}[/latex-display]

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