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$5x+y=10$
ⓑ , ⓒ
$y=6x-2$
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.
$y=4x-1$
$x$ | $y$ | $(x,y)$ |
---|---|---|
$0$ | ||
$1$ | ||
$\mathrm{-2}$ |
$x$ | $y$ | $(x,y)$ |
---|---|---|
$0$ | $\mathrm{-1}$ | $\left(0,\mathrm{-1}\right)$ |
$1$ | $3$ | $\left(1,3\right)$ |
$\mathrm{-2}$ | $\mathrm{-9}$ | $\left(\mathrm{-2},\mathrm{-9}\right)$ |
$y=-\frac{1}{2}x+3$
$x$ | $y$ | $(x,y)$ |
---|---|---|
$0$ | ||
$1$ | ||
$\mathrm{-2}$ |
$x+2y=5$
$x$ | $y$ | $(x,y)$ |
---|---|---|
$0$ | ||
$1$ | ||
$\mathrm{-1}$ |
$x$ | $y$ | $(x,y)$ |
---|---|---|
$5$ | $0$ | $\left(5,0\right)$ |
$1$ | $2$ | $\left(1,2\right)$ |
$\mathrm{-1}$ | $3$ | $\left(\mathrm{-1},3\right)$ |
$3x-2y=6$
$x$ | $y$ | $(x,y)$ |
---|---|---|
$0$ | ||
$0$ | ||
$\mathrm{-2}$ |
Find Solutions to a Linear Equation in Two Variables
In the following exercises, find three solutions to each linear equation.
$x+y=\mathrm{-4}$
Recognize the Relation Between the Solutions of an Equation and its Graph
In the following exercises, for each ordered pair, decide
$y=-x+4$
$y=\frac{2}{3}x-1$
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.
$y=\mathrm{-2}$
Identify the Intercepts on a Graph
In the following exercises, find the $x\text{-}$ and $y\text{-intercepts}.$
Find the Intercepts from an Equation of a Line
In the following exercises, find the intercepts.
$y=\frac{3}{4}x-12$
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.
$y=\frac{1}{2}x+2$
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.
$x=\mathrm{-3}$
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?
Plot and label these points:
Name the ordered pair for each point shown.
Find the $x\text{-intercept}$ and $y\text{-intercept}$ on the line shown.
(4,0), (0,−2)
Find the $x\text{-intercept}$ and $y\text{-intercept}$ of the equation $3x-y=6.$
Is $\left(1,3\right)$ a solution to the equation $x+4y=12?$ How do you know?
no; 1 + 4 · 3 ≠ 12
Complete the table to find four solutions to the equation $y=-x+1.$
$x$ | $y$ | $(x,y)$ |
$0$ | ||
$1$ | ||
$3$ | ||
$\mathrm{-2}$ |
Complete the table to find three solutions to the equation $4x+y=8$
$x$ | $y$ | $(x,y)$ |
$0$ | ||
$0$ | ||
$3$ |
$x$ | $y$ | $(x,y)$ |
$0$ | $8$ | $(0,8)$ |
$2$ | $0$ | $(2,0)$ |
$3$ | $\mathrm{-4}$ | $(3,\mathrm{-4})$ |
In the following exercises, find three solutions to each equation and then graph each line.
$y=\mathrm{-3}x$
In the following exercises, find the slope of each line.
Use the slope formula to find the slope of the line between $\left(0,\mathrm{-4}\right)$ and $\left(5,2\right).$
Graph the line passing through $\left(1,1\right)$ with slope $m=\frac{3}{2}.$
A bicycle route climbs $20$ feet for $\mathrm{1,000}$ feet of horizontal distance. What is the slope of the route?
$\frac{1}{50}$
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