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Identify the slope and y -intercept of the line y = 2 5 x 1 .

2 5 ; ( 0 , −1 )

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Identify the slope and y -intercept of the line y = 4 3 x + 1 .

4 3 ; ( 0 , 1 )

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When an equation of a line is not given in slope–intercept form, our first step will be to solve the equation for y .

Identify the slope and y -intercept of the line with equation x + 2 y = 6 .

Solution

This equation is not in slope–intercept form. In order to compare it to the slope–intercept form we must first solve the equation for y .

Solve for y . x + 2 y = 6
Subtract x from each side. .
Divide both sides by 2. .
Simplify. .
( Remember: a + b c = a c + b c )
Simplify. .
Write the slope–intercept form of the equation of the line. .
Write the equation of the line. .
Identify the slope. .
Identify the y -intercept. .

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Identify the slope and y -intercept of the line x + 4 y = 8 .

1 4 ; ( 0 , 2 )

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Identify the slope and y -intercept of the line 3 x + 2 y = 12 .

3 2 ; ( 0 , 6 )

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Graph a line using its slope and intercept

Now that we know how to find the slope and y -intercept of a line from its equation, we can graph the line by plotting the y -intercept and then using the slope to find another point.

How to graph a line using its slope and intercept

Graph the line of the equation y = 4 x 2 using its slope and y -intercept.

Solution

The figure shows the steps to graph the equation y equals 4x minus 2. Step 1 is to find the slope intercept form of the equation. The equation is already in slope intercept form. Step 2 is to identify the slope and y-intercept. Use the equation y equals m x, plus b. The equation y equals m x, plus b is shown with the variable m colored red and the variable b colored blue. Below that is the equation y equals 4 x, plus -2. The number 4 is colored red and -2 is colored blue. From this equation we can see that m equals 4 and b equals -2 so the slope is 4 and the y-intercept is the point (0, negative 2). Step 3 is to plot the y-intercept. An x y-coordinate plane is shown with the x-axis of the plane running from negative 8 to 8. The y-axis of the plane runs from negative 8 to 8. The point (0, negative 2) is plotted. Step 4 is to use the slope formula m equals rise over run to identify the rise and the run. Since m equals 4, rise over run equals 4 over 1. From this we can determine that the rise is 4 and the run is 1. Step 5 is to start at they-intercept, count out the rise and run to mark the second point. So start at the point (0, negative 2) and count the rise and the run. The rise is up 4 and the run is right 1. On the x y-coordinate plane is a red vertical line starts at the point (0, negative 2) and rises 4 units at its end a red horizontal line runs 1 unit to end at the point (1, 2). The point (1, 2)  is plotted. Step 6 is to connect the points with a line. On the x y-coordinate plane the points (0, negative 2) and (1, 2) are plotted and a line runs through the two points. The line is the graph of y equals 4 x, minus 2.
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Graph the line of the equation y = 4 x + 1 using its slope and y -intercept.

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, 1) and (1, 5) are plotted on the line.

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Graph the line of the equation y = 2 x 3 using its slope and y -intercept.

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 3) and (1, negative 1) are plotted on the line.

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Graph a line using its slope and y -intercept.

  1. Find the slope-intercept form of the equation of the line.
  2. Identify the slope and y -intercept.
  3. Plot the y -intercept.
  4. Use the slope formula m = rise run to identify the rise and the run.
  5. Starting at the y -intercept, count out the rise and run to mark the second point.
  6. Connect the points with a line.

Graph the line of the equation y = x + 4 using its slope and y -intercept.

Solution

y = m x + b
The equation is in slope–intercept form. y = x + 4
Identify the slope and y -intercept. m = −1
y -intercept is (0, 4)
Plot the y -intercept. See graph below.
Identify the rise and the run. m = −1 1
Count out the rise and run to mark the second point. rise −1, run 1
Draw the line. .
To check your work, you can find another point on the line and make sure it is a solution of the equation. In the graph we see the line goes through (4, 0).
Check.
y = x + 4 0 = ? 4 + 4 0 = 0

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Graph the line of the equation y = x 3 using its slope and y -intercept.

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 3) and (1, negative 4) are plotted on the line.

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Graph the line of the equation y = x 1 using its slope and y -intercept.

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 1) and (1, negative 2) are plotted on the line.

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Graph the line of the equation y = 2 3 x 3 using its slope and y -intercept.

Solution

y = m x + b
The equation is in slope–intercept form. y = 2 3 x 3
Identify the slope and y -intercept. m = 2 3 ; y -intercept is (0, −3)
Plot the y -intercept. See graph below.
Identify the rise and the run.
Count out the rise and run to mark the second point.
Draw the line. .

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Graph the line of the equation y = 5 2 x + 1 using its slope and y -intercept.

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0,1) and (2, negative 4) are plotted on the line.

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Graph the line of the equation y = 3 4 x 2 using its slope and y -intercept.

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, negative 2) and (4, negative 5) are plotted on the line.

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Graph the line of the equation 4 x 3 y = 12 using its slope and y -intercept.

Solution

4 x 3 y = 12
Find the slope–intercept form of the equation. −3 y = −4 x + 12
3 y 3 = −4 x + 12 −3
The equation is now in slope–intercept form. y = 4 3 x 4
Identify the slope and y -intercept. m = 4 3
y -intercept is (0, −4)
Plot the y -intercept. See graph below.
Identify the rise and the run; count out the rise and run to mark the second point.
Draw the line. .

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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