### 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.

$\left(2,5\right),\left(5,2\right)$

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

- ⓐ $\phantom{\rule{0.2em}{0ex}}(\mathrm{-1},\mathrm{-5})$
- ⓑ $\phantom{\rule{0.2em}{0ex}}(\mathrm{-3},4)$
- ⓒ $\phantom{\rule{0.2em}{0ex}}\left(2,\mathrm{-3}\right)$
- ⓓ $\phantom{\rule{0.2em}{0ex}}\left(1,\frac{5}{2}\right)$

- ⓐ $\phantom{\rule{0.2em}{0ex}}\left(3,\mathrm{-2}\right)$
- ⓑ $\phantom{\rule{0.2em}{0ex}}\left(\mathrm{-4},\mathrm{-1}\right)$
- ⓒ $\phantom{\rule{0.2em}{0ex}}\left(\mathrm{-5},4\right)$
- ⓓ $\phantom{\rule{0.2em}{0ex}}\left(2,\frac{10}{3}\right)$

**Identify Points on a Graph**

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.

**Verify Solutions to an Equation in Two Variables**

In the following exercises, find the ordered pairs that are solutions to the given equation.

$5x+y=10$

- ⓐ $\phantom{\rule{0.2em}{0ex}}(5,1)$
- ⓑ $\phantom{\rule{0.2em}{0ex}}(2,0)$
- ⓒ $\phantom{\rule{0.2em}{0ex}}(4,\mathrm{-10})$

$y=6x-2$

- ⓐ $\phantom{\rule{0.2em}{0ex}}(1,4)$
- ⓑ $\phantom{\rule{0.2em}{0ex}}\left(\frac{1}{3},0\right)$
- ⓒ $\phantom{\rule{0.2em}{0ex}}(6,\mathrm{-2})$

**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.

$y=-\frac{1}{2}x+3$

$x$ | $y$ | $(x,y)$ |
---|---|---|

$0$ | ||

$1$ | ||

$\mathrm{-2}$ |

$3x-2y=6$

$x$ | $y$ | $(x,y)$ |
---|---|---|

$0$ | ||

$0$ | ||

$\mathrm{-2}$ |

**Find Solutions to a Linear Equation in Two Variables**

In the following exercises, find three solutions to each linear equation.

$x+y=\mathrm{-4}$

$y=-x-1$

##### Graphing Linear Equations

**Recognize the Relation Between the Solutions of an Equation and its Graph**

In each of the following exercises, an equation and its graph is shown. For each ordered pair, decide

- ⓐ if the ordered pair is a solution to the equation.
- ⓑ if the point is on the line.

$y=-x+4$

- $\phantom{\rule{0.2em}{0ex}}(0,4)$
- $\phantom{\rule{0.2em}{0ex}}(\mathrm{-1},3)$
- $\phantom{\rule{0.2em}{0ex}}(2,2)$
- $\phantom{\rule{0.2em}{0ex}}(\mathrm{-2},6)$

$y=\frac{2}{3}x-1$

- $\phantom{\rule{0.2em}{0ex}}(0,\mathrm{-1})$
- $\phantom{\rule{0.2em}{0ex}}(3,1)$
- $\phantom{\rule{0.2em}{0ex}}(\mathrm{-3},\mathrm{-3})$
- $\phantom{\rule{0.2em}{0ex}}(6,4)$

**Graph a Linear Equation by Plotting Points**

In the following exercises, graph by plotting points.

$y=\mathrm{-3}x$

**Graph Vertical and Horizontal lines**

In the following exercises, graph the vertical or horizontal lines.

$y=\mathrm{-2}$

##### Graphing with Intercepts

**Identify the Intercepts on a Graph**

In the following exercises, find the $x-$ and $y\text{-intercepts}.$

**Find the Intercepts from an Equation of a Line**

In the following exercises, find the intercepts.

$x+y=5$

$y=\frac{3}{4}x-12$

**Graph a Line Using the Intercepts**

In the following exercises, graph using the intercepts.

$-x+3y=3$

**Choose the Most Convenient Method to Graph a Line**

In the following exercises, identify the most convenient method to graph each line.

$x=5$

$2x+y=5$

$y=\frac{1}{2}x+2$

##### Understand Slope of a Line

**Use Geoboards to Model Slope**

In the following exercises, find the slope modeled on each geoboard.

In the following exercises, model each slope. Draw a picture to show your results.

$\frac{1}{3}$

$-\frac{2}{3}$

**Find the Slope of a Line from its Graph**

In the following exercises, find the slope of each line shown.

**Find the Slope of Horizontal and Vertical Lines**

In the following exercises, find the slope of each line.

$y=2$

$x=\mathrm{-3}$

**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.

$(2,1),(4,5)$

$(3,5),(4,\mathrm{-1})$

**Graph a Line Given a Point and the Slope**

In the following exercises, graph the line given a point and the slope.

$(2,\mathrm{-2});m=\frac{5}{2}$

**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?