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# Why It Matters: The Rectangular Coordinate System and Equations of Lines

## Why learn about The Rectangular Coordinate System?

Caroline is a full-time college student planning a spring break vacation. To earn enough money for the trip, she has taken a part-time job at the local bank that pays $15.00/hr, and she opened a savings account with an initial deposit of$400 on January 15. She arranged for direct deposit of her payroll checks. If spring break begins March 20 and the trip will cost approximately \$2,500, how many hours will she have to work to earn enough to pay for her vacation? If she can only work 4 hours per day, how many days per week will she have to work? How many weeks will it take? In this section, we will investigate problems like this and others, which generate graphs like the line in the figure below.
Figure 1

### Learning Objectives

Points and Lines in the Plane
• Plot ordered pairs, and graph equations by plotting points
• Use a graphing utility to graph equations
• Find the x and y intercepts of a graphed equation
• Use the distance and midpoint formulas

Equations of Lines

• Write equations of lines in slope-intercept, point-slope, and standard forms
• Identify the equations and graphs of horizontal and vertical lines
• Determine whether two lines are parallel, perpendicular, or neither
• Write equations of lines that are parallel or perpendicular to another line