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5 x + y = 10

  1. ( 5 , 1 )
  2. ( 2 , 0 )
  3. ( 4 , −10 )

,

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y = 6 x 2

  1. ( 1 , 4 )
  2. ( 1 3 , 0 )
  3. ( 6 , −2 )
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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 = 4 x 1

x y ( x , y )
0
1
−2
x y ( x , y )
0 −1 ( 0 , −1 )
1 3 ( 1 , 3 )
−2 −9 ( −2 , −9 )
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y = 1 2 x + 3

x y ( x , y )
0
1
−2
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x + 2 y = 5

x y ( x , y )
0
1
−1
x y ( x , y )
5 0 ( 5 , 0 )
1 2 ( 1 , 2 )
−1 3 ( −1 , 3 )
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3 x 2 y = 6

x y ( x , y )
0
0
−2
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Find Solutions to a Linear Equation in Two Variables

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

x + y = 3

Answers will vary.

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y = 3 x + 1

Answers will vary.

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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. ( 0 , 4 )
  2. ( −1 , 3 )
  3. ( 2 , 2 )
  4. ( −2 , 6 )
The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0,  4” and “ordered pair 4, 0”.

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

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y = 2 3 x 1

  1. ( 0 , −1 )
  2. ( 3 , 1 )
  3. ( −3 , −3 )
  4. ( 6 , 4 )
The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0,  -1” and “ordered pair 3, 1”.
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Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

Graph Vertical and Horizontal lines

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

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 = −1

(−1,0) (0,1)

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Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

Choose the Most Convenient Method to Graph a Line

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

y = −3

horizontal line

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y = 3 4 x 1

plotting points

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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.

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.

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.

( −1 , −1 ) , ( 0 , −5 )

−4

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( 3 , 5 ) , ( 4 , −1 )

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( −5 , −2 ) , ( 3 , 2 )

1 2

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Graph a Line Given a Point and the Slope

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

( −3 , 4 ) ; m = 1 3


The graph shows the x y-coordinate plane. The x-axis runs from -6 to 6. The y-axis runs from -4 to 2. A line passes through the points “ordered pair -3,  4” and “ordered pair 1, 3”.

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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?

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Chapter practice test

Plot and label these points:

  1. ( 2 , 5 )
  2. ( −1 , −3 )
  3. ( −4 , 0 )
  4. ( 3 , −5 )
  5. ( −2 , 1 )


The graph shows the x y-coordinate plane. The axes extend from -6 to 6. a is plotted at 2, 5, b at -1, -3, c at -4, 0, d at 3, -5, and e at -2,1.

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Name the ordered pair for each point shown.

The graph shows the x y-coordinate plane. The axes extend from -7 to 7. A is plotted at -4, 1, B at 3, 2, C at 0, -2, D at -1, -4, and E at 4,-3.
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Find the x -intercept and y -intercept on the line shown.

 The graph shows the x y-coordinate plane. The x-axis runs from -7 to 7. The y-axis runs from -7 to 7. A line passes through the points “ordered pair 4,  0” and “ordered pair 0, -2”.

(4,0), (0,−2)

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Find the x -intercept and y -intercept of the equation 3 x y = 6 .

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Is ( 1 , 3 ) a solution to the equation x + 4 y = 12 ? How do you know?

no; 1 + 4 · 3 ≠ 12

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Complete the table to find four solutions to the equation y = x + 1 .

x y ( x , y )
0
1
3
−2
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Complete the table to find three solutions to the equation 4 x + y = 8

x y ( x , y )
0
0
3
x y ( x , y )
0 8 ( 0 , 8 )
2 0 ( 2 , 0 )
3 −4 ( 3 , −4 )
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In the following exercises, find three solutions to each equation and then graph each line.

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 ) .

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Find the slope of the line y = 2 .

0

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Graph the line passing through ( 1 , 1 ) with slope m = 3 2 .

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

1 50

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Questions & Answers

explain and give four Example hyperbolic function
Lukman Reply
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
SABAL Reply
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?
mariel Reply
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?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
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
yes i wantt to review
Mark
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
please help me prove quadratic formula
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
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
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-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
Alfred Reply
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.
Kimberly Reply
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.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
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)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 1

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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