# 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
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
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Abdullahi
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Mark
find the value of 2x=32
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
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Mark
use the y -intercept and slope to sketch the graph of the equation y=6x
how do we prove the quadratic formular
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
thank you help me with how to prove the quadratic equation
Seidu
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Opoku
what is math number
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?

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