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.
Learning Outcomes
Review Topics- Use properties of equality to isolate variables and solve algebraic equations
- Solve equations containing absolute value
- Use the properties of equality and the distributive property to solve equations containing parentheses
- Clear fractions and decimals from equations to make them easier to solve
- Identify equations that have one solution, no solution, or an infinite number of solutions
- Recognize when a linear equation that contains absolute value does not have a solution
Points and Lines in the Plane
- Define the components of the Cartesian coordinate system.
- Plot points on the Cartesian coordinate plane.
- Use the distance formula to find the distance between two points in the plane.
- Use the midpoint formula to find the midpoint between two points.
- Plot linear equations in two variables on the coordinate plane.
- Use intercepts to plot lines.
- Use a graphing utility to graph a linear equation on a coordinate plane.
Equations of Lines
- Use slope-intercept form to plot and write equations of lines.
- Use point-slope form to write the equation of a line.
- Write the equation of a line in standard form.
- Recognize vertical and horizontal lines from their graphs and equations.
- Determine whether two lines are parallel or perpendicular.
- Find the equations of parallel and perpendicular lines.
- Write the equations of lines that are parallel or perpendicular to a given line.
Licenses & Attributions
CC licensed content, Shared previously
- College Algebra. Authored by: OpenStax College Algebra. Located at: https://openstax.org/books/college-algebra/pages/2-2-linear-equations-in-one-variable. License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].
