<meta http-equiv="refresh" content="1; url=/nojavascript/"> Graph a Line in Standard Form | CK-12 Foundation
Dismiss
Skip Navigation
You are reading an older version of this FlexBook® textbook: CK-12 Algebra II with Trigonometry Concepts Go to the latest version.

2.7: Graph a Line in Standard Form

Difficulty Level: At Grade / At Grade / Basic / Basic / Basic / Advanced Created by: CK-12
%
Best Score
Practice Graphs of Linear Equations
Practice
Best Score
%
Practice Now

Scott and Brooke are organizing a fundraiser for their school. They are planning a pasta dinner, where adult tickets will cost $16 and kids' tickets will cost $8. Their goal is to make $2000. If they sell only adult tickets, how many must they sell to reach their goal? If they sell only kids' tickets, how many must they sell to reach their goal?

Guidance

When a line is in standard form, there are two different ways to graph it. The first is to change the equation to slope-intercept form and then graph as shown in the previous concept. The second is to use standard form to find the x and y- intercepts of the line and connect the two. Here are a few examples.

Example A

Graph 5x - 2y = -15 .

Solution: Let’s use approach #1; change the equation to slope-intercept form.

5x -2y &= -15\\-2y &= -5x - 15\\y &= \frac{5}{2}x + \frac{15}{2}

The y- intercept is \left( 0, \frac{15}{2} \right) . Change the improper fraction to a decimal and approximate it on the graph, (0, 7.5). Then use slope triangles. If you find yourself running out of room “rising 5” and “running 2,” you could also “fall 5” and “run backwards 2” to find a point on the other side of the y- intercept.

Example B

Find the x and y intercepts of the equation 4x - 3x = 21 .

Solution: Recall the Standard Form of a Line concept. The other coordinate will be zero at these points. Therefore, for the x- intercept, plug in zero for y and for the y- intercept, plug in zero for x .

4x - 3(0) &= 21 && 4(0) -3y = 21\\4x &= 21 && \quad \ \ -3y = 21\\x &= \frac{21}{4} \ or \ 5.25 && \qquad \quad \ y = -7

Example C

Graph the equation from Example B .

Solution: Use approach #2 from above. Plot each intercept from Example B on their respective axes and draw a line to connect them.

Intro Problem Revisit The equation, in standard form, for the pasta dinner sales goal is 2000 = 16x + 8y . If they sell only adult tickets, we are looking for the x -intercept, so set y equal to zero.

2000 = 16x + 8(0)\\2000 = 16x\\x = 125

Therefore, they must sell 125 adult tickets to reach their goal.

If they sell only kids' tickets, we are looking for the y -intercept, so set x equal to zero.

2000 = 16(0) + 8y\\2000 = 8y\\y = 250

Therefore, they must sell 250 kids' tickets to reach their goal.

Guided Practice

1. Graph 4x + 6y = 18 by changing it into slope-intercept form.

2. Graph 5x - 3y = 30 by plotting the intercepts.

Answers

1. Change 4x + 6y = 18 into slope-intercept form by solving for y , then graph.

4x +6y &= 18\\6y &= -4x + 18\\y &= - \frac{2}{3}x + 3

2. Substitute in zero for x , followed by y and solve each equation.

5(0) - 3y &= 30 && 5x -3(0) = 30\\-3y &= 30 && \qquad \quad 5x = 30\\y &= -10 && \qquad \quad \ x = 6

Now, plot each on their respective axes and draw a line.

Practice

Graph the following lines by changing the equation to slope-intercept form.

  1. -2x + y = 5
  2. 3x + 8y = 16
  3. 4x -2y = 10
  4. 6x + 5y = -20
  5. 9x - 6y = 24
  6. x + 4y = -12

Graph the following lines by finding the intercepts.

  1. 2x + 3y = 12
  2. -4x + 5y = 30
  3. x - 2y = 8
  4. 7x + y = -7
  5. 6x + 10y = 15
  6. 4x -8y = -28
  7. y=3
  8. Writing Which method do you think is easier? Why?
  9. Writing Which method would you use to graph x = -5 ? Why?

Image Attributions

Description

Difficulty Level:

At Grade

Grades:

Date Created:

Mar 12, 2013

Last Modified:

Feb 23, 2014
Files can only be attached to the latest version of Modality

Reviews

Please wait...
You need to be signed in to perform this action. Please sign-in and try again.
Please wait...
Image Detail
Sizes: Medium | Original
 
MAT.ALG.451.L.4

Original text