# Linear Functions Practice Test

1. Determine whether the following algebraic equation can be written as a linear function. 2*x *+ 3*y *= 7
2. Determine whether the following function is increasing or decreasing. *f*(*x*) = –2*x* + 5
3. Determine whether the following function is increasing or decreasing. *f*(*x*) = 7*x *+ 9
4. Given the following set of information, find a linear equation satisfying the conditions, if possible.
Passes through (5, 1) and (3, –9)
5. Given the following set of information, find a linear equation satisfying the conditions, if possible.
x intercept at (–4, 0) and y-intercept at (0, –6)
6. Find the slope of the line in the graph below.
7. Write an equation for line in the graph below.
8. Does the table below represent a linear function? If so, find a linear equation that models the data.

x |
–6 | 0 | 2 | 4 |

g(x) |
14 | 32 | 38 | 44 |

x |
1 | 3 | 7 | 11 |

g(x) |
4 | 9 | 19 | 12 |

*x*+ 7

*y*= –14. 14. Given below are descriptions of two lines. Find the slopes of Line 1 and Line 2. Is the pair of lines parallel, perpendicular, or neither? Line 1: Passes through (–2, –6) and (3, 14) Line 2: Passes through (2, 6) and (4, 14) 15. Write an equation for a line perpendicular to

*f*(

*x*) = 4

*x*+ 3 and passing through the point (8, 10). 16. Sketch a line with a y-intercept of (0, 5) and slope [latex]-\frac{5}{2}\\[/latex] . 17. Graph the linear function

*f*(

*x*) = –

*x*+ 6 . 18. For the two linear functions, find the point of intersection: [latex]\begin{cases}x=y+2\\ 2x - 3y=-1\end{cases}\\[/latex] 19. A car rental company offers two plans for renting a car. Plan A: $25 per day and $0.10 per mile Plan B: $40 per day with free unlimited mileage How many miles would you need to drive for plan B to save you money? 20. Find the area of a triangle bounded by the y axis, the line

*f*(

*x*) = 12 – 4

*x*, and the line perpendicular to

*f*that passes through the origin. 21. A town’s population increases at a constant rate. In 2010 the population was 65,000. By 2012 the population had increased to 90,000. Assuming this trend continues, predict the population in 2018. 22. The number of people afflicted with the common cold in the winter months dropped steadily by 25 each year since 2002 until 2012. In 2002, 8,040 people were inflicted. Find the linear function that models the number of people afflicted with the common cold

*C*as a function of the year,

*t*. When will less than 6,000 people be afflicted? For the following exercises, use the graph below, showing the profit,

*y*, in thousands of dollars, of a company in a given year,

*x*, where

*x*represents years since 1980. 23. Find the linear function

*y*, where

*y*depends on

*x*, the number of years since 1980. 24. Find and interpret the

*y*-intercept. 25. In 2004, a school population was 1250. By 2012 the population had dropped to 875. Assume the population is changing linearly.

a. How much did the population drop between the year 2004 and 2012?
b. What is the average population decline per year?
c. Find an equation for the population, *P*, of the school *t* years after 2004.

0 | 2 | 4 | 6 | 8 | 10 |

–450 | –200 | 10 | 265 | 500 | 755 |

Year |
Percent Graduates |

2000 | 8.5 |

2002 | 8.0 |

2005 | 7.2 |

2007 | 6.7 |

2010 | 6.4 |

x |
16 | 18 | 20 | 24 | 26 |

y |
106 | 110 | 115 | 120 | 125 |

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**Provided by:**OpenStax**Authored by:**Jay Abramson, et al..**Located at:**https://openstax.org/books/precalculus/pages/1-introduction-to-functions.**License:**CC BY: Attribution.**License terms:**Download For Free at : http://cnx.org/contents/[email protected]..