11.1 - Use the Rectangular Coordinate System
Plot Points in a Rectangular Coordinate System
In the following exercises, plot each point in a rectangular coordinate system.
- (1, 3), (3, 1)
- (2, 5), (5, 2)
In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.
- (a) (−1, −5) (b) (−3, 4) (c) (2, −3) (d) \(\left(1, \dfrac{5}{2}\right)\)
- (a) (3, −2) (b) (−4, −1) (c) (−5, 4) (d) \(\left(2, \dfrac{10}{3}\right)\)
Verify Solutions to an Equation in Two Variables
In the following exercises, find the ordered pairs that are solutions to the given equation.
- 5x + y = 10
- (5, 1)
- (2, 0)
- (4, −10)
- y = 6x − 2
- (1, 4)
- \(\left(\dfrac{1}{3} , 0\right)\)
- (6, −2)
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.
- y = 4x − 1
- y = \(− \dfrac{1}{2}\)x + 3
- x + 2y = 5
- 3x − 2y = 6
Find Solutions to a Linear Equation in Two Variables
In the following exercises, find three solutions to each linear equation.
- x + y = 3
- x + y = −4
- y = 3x + 1
- y = − x − 1
11.2 - Graphing Linear Equations
Recognize the Relation Between the Solutions of an Equation and its Graph
In the following exercises, for each ordered pair, decide (a) if the ordered pair is a solution to the equation. (b) if the point is on the line.
- y = − x + 4
- (0, 4)
- (−1, 3)
- (2, 2)
- (−2, 6)

- y = \(\dfrac{2}{3}\)x − 1
- (0, −1)
- (3, 1)
- (−3, −3)
- (6, 4)

Graph a Linear Equation by Plotting Points
In the following exercises, graph by plotting points.
- y = 4x − 3
- y = −3x
- 2x + y = 7
Graph Vertical and Horizontal lines
In the following exercises, graph the vertical or horizontal lines.
- y = −2
- x = 3
11.3 - Graphing with Intercepts
Identify the Intercepts on a Graph
In the following exercises, find the x- and y-intercepts.


Find the Intercepts from an Equation of a Line
In the following exercises, find the intercepts.
- x + y = 5
- x − y = −1
- y = \(\dfrac{3}{4}\)x − 12
- y = 3x
Graph a Line Using the Intercepts
In the following exercises, graph using the intercepts.
- −x + 3y = 3
- x + y = −2
Choose the Most Convenient Method to Graph a Line
In the following exercises, identify the most convenient method to graph each line.
- x = 5
- y = −3
- 2x + y = 5
- x − y = 2
- y = \(\dfrac{1}{2}\)x + 2
- y = \(\dfrac{3}{4}\)x − 1
11.4 - Understand Slope of a Line
Find the Slope of Horizontal and Vertical Lines
In the following exercises, find the slope of each line.
- y = 2
- x = 5
- x = −3
- y = −1
In the following exercises, use the slope formula to find the slope of the line between each pair of points.
- (2, 1), (4, 5)
- (−1, −1), (0, −5)
- (3, 5), (4, −1)
- (−5, −2), (3, 2)
Graph a Line Given a Point and the Slope
In the following exercises, graph the line given a point and the slope.
- (2, −2); m = \(\dfrac{5}{2}\)
- (−3, 4); m = \(− \dfrac{1}{3}\)
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?
PRACTICE TEST
- Plot and label these points:
- (2, 5)
- (−1, −3)
- (−4, 0)
- (3, −5)
- (−2, 1)
- Name the ordered pair for each point shown.

- Find the x-intercept and y-intercept on the line shown.

- Find the x-intercept and y-intercept of the equation 3x − y = 6.
- Is (1, 3) a solution to the equation x + 4y = 12? How do you know?
- Complete the table to find four solutions to the equation y = − x + 1.
- Complete the table to find three solutions to the equation 4x + y = 8.
In the following exercises, find three solutions to each equation and then graph each line.
- y = −3x
- 2x + 3y = −6
In the following exercises, find the slope of each line.


- Use the slope formula to find the slope of the line between (0, −4) and (5, 2).
- Find the slope of the line y = 2.
- Graph the line passing through (1, 1) with slope m = \(\dfrac{3}{2}\).
- A bicycle route climbs 20 feet for 1,000 feet of horizontal distance. What is the slope of the route?