# 11.4 Understand slope of a line  (Page 8/9)

 Page 8 / 9

$5x+y=10$

1. $\phantom{\rule{0.2em}{0ex}}\left(5,1\right)$
2. $\phantom{\rule{0.2em}{0ex}}\left(2,0\right)$
3. $\phantom{\rule{0.2em}{0ex}}\left(4,-10\right)$

,

$y=6x-2$

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

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.

$y=4x-1$

$x$ $y$ $\left(x,y\right)$
$0$
$1$
$-2$
$x$ $y$ $\left(x,y\right)$
$0$ $-1$ $\left(0,-1\right)$
$1$ $3$ $\left(1,3\right)$
$-2$ $-9$ $\left(-2,-9\right)$

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

$x$ $y$ $\left(x,y\right)$
$0$
$1$
$-2$

$x+2y=5$

$x$ $y$ $\left(x,y\right)$
$0$
$1$
$-1$
$x$ $y$ $\left(x,y\right)$
$5$ $0$ $\left(5,0\right)$
$1$ $2$ $\left(1,2\right)$
$-1$ $3$ $\left(-1,3\right)$

$3x-2y=6$

$x$ $y$ $\left(x,y\right)$
$0$
$0$
$-2$

Find Solutions to a Linear Equation in Two Variables

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

$x+y=3$

$x+y=-4$

$y=3x+1$

$y=-x-1$

## Graphing Linear Equations

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

In the following exercises, for each ordered pair, decide

1. if the ordered pair is a solution to the equation.
2. if the point is on the line.

$y=-x+4$

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

1. yes no yes yes
2. yes no yes yes

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

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

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.

$y=-2$

$x=3$

## Graphing with Intercepts

Identify the Intercepts on a Graph

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

(0,3) (3,0)

Find the Intercepts from an Equation of a Line

In the following exercises, find the intercepts.

$x+y=5$

$x-y=-1$

(−1,0) (0,1)

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

$y=3x$

(0,0)

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.

$x=5$

$y=-3$

horizontal line

$2x+y=5$

$x-y=2$

intercepts

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

$y=\frac{3}{4}x-1$

plotting points

## Understand Slope of a Line

Use Geoboards to Model Slope

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

$\frac{4}{3}$

$-\frac{2}{3}$

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

$\frac{1}{3}$

$\frac{3}{2}$

$-\frac{2}{3}$

$-\frac{1}{2}$

Find the Slope of a Line from its Graph

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

1

$-\frac{1}{2}$

Find the Slope of Horizontal and Vertical Lines

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

$y=2$

$x=5$

undefined

$x=-3$

$y=-1$

0

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.

$\left(2,1\right),\left(4,5\right)$

$\left(-1,-1\right),\left(0,-5\right)$

−4

$\left(3,5\right),\left(4,-1\right)$

$\left(-5,-2\right),\left(3,2\right)$

$\frac{1}{2}$

Graph a Line Given a Point and the Slope

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

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

$\left(-3,4\right);m=-\frac{1}{3}$

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?

## Chapter practice test

Plot and label these points:

1. $\phantom{\rule{0.2em}{0ex}}\left(2,5\right)$
2. $\phantom{\rule{0.2em}{0ex}}\left(-1,-3\right)$
3. $\phantom{\rule{0.2em}{0ex}}\left(-4,0\right)$
4. $\phantom{\rule{0.2em}{0ex}}\left(3,-5\right)$
5. $\phantom{\rule{0.2em}{0ex}}\left(-2,1\right)$

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 $y=-x+1.$

 $x$ $y$ $\left(x,y\right)$ $0$ $1$ $3$ $-2$

Complete the table to find three solutions to the equation $4x+y=8$

 $x$ $y$ $\left(x,y\right)$ $0$ $0$ $3$
 $x$ $y$ $\left(x,y\right)$ $0$ $8$ $\left(0,8\right)$ $2$ $0$ $\left(2,0\right)$ $3$ $-4$ $\left(3,-4\right)$

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.

$-\frac{5}{2}$

Use the slope formula to find the slope of the line between $\left(0,-4\right)$ and $\left(5,2\right).$

Find the slope of the line $y=2.$

0

Graph the line passing through $\left(1,1\right)$ with slope $m=\frac{3}{2}.$

A bicycle route climbs $20$ feet for $1,000$ feet of horizontal distance. What is the slope of the route?

$\frac{1}{50}$

explain and give four Example hyperbolic function
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
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