5| Step 3: Graphing by Slope-Intercept

5| Step 3: Graphing by Slope-Intercept

By Maria Leon

The y variable should be isolated on the left side.

The m is always paired with the x. This m is the slope.

The b is the y-intercept of the graph.​

Slope-intercept form

First cancel out the mx term by the opposite operation of either addition or subtraction.

Second, divide both sides by the coefficient of y.​

Rewriting from Standard to Slope-intercept

1. Cancel mx - Here we add 3x to both sides.

2. Divide both sides by the coefficient of y - Here we divide both sides by 2.​ Notice that on the right side, we distribute the division. So the 20 is divided by 2, and also the 3x is divided by 2.

Another Example

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Rewrite this equation in slope-intercept form.

$$3x+2y=10$$  

First step: Cancel the mx on the left side. Make sure to mirror your moves on the right side of the equation as well.

Note: Your answer should be what the equation would look like after the mx is cancelled.

Example: -7y=2x+5

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Rewrite this equation in slope-intercept form.

$$3x+2y=10$$  

Second step: Divide both sides of the equation with the coefficient of y.

Note: Your answer should be what the equation should be in its final slope-intercept form.

Example: y=-2/7x+3

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Rewrite this equation in slope-intercept form.

$$5x-3y=9$$  

First step: Cancel the mx on the left side.

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Rewrite this equation in slope-intercept form.

$$5x-3y=9$$  

Second step: Divide both sides with the coefficient of y.

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Rewrite this equation in slope-intercept form.

$$2x+4y=-8$$  

First step: Cancel the mx on the left side.

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Rewrite this equation in slope-intercept form.

$$2x+4y=-8$$  

Second step: Divide both sides with the coefficient of y.

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Rewrite this equation in slope-intercept form.

$$5x-2y=-16$$  

First step: Cancel the mx on the left side.

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Rewrite this equation in slope-intercept form.

$$5x-2y=-16$$  

Second step: Divide both sides with the coefficient of y.

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Rewrite this equation in slope-intercept form.

$$-6x+3y=18$$  

First step: Cancel the mx on the left side.

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Rewrite this equation in slope-intercept form.

$$-6x+3y=18$$  

Second step: Divide both sides with the coefficient of y.

First, find the slope of the graph by counting the rise over run from one point to the next.

Second, get the y-intercept.

Then substitute these values into the m and b of the equation.​

Writing equations from graphs

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What is the rise of the equation?

Count upward (or downward) from the location of the left red point to the next red point.

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What is the run of the equation?

Count from left to right from the location of the left red point to the next red point.

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What is the slope of the equation?

Put together the rise and run to get the slope. Make sure you use the format $$m=\frac{rise}{run}$$ .

Don't forget your answer must be in SIMPLEST FORM.

Do NOT put spaces in your answer.

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What is the y-intercept of the graph?

Write your answer as an ordered pair. Do not put spaces.

Example: (0,3)

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What is the equation of this graph in slope-intercept form $$y=mx+b$$  ?

Just replace m with the slope and b with the y-coordinate of the y-intercept.

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What is the rise of this graph?

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What is the run of this graph?

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What is the slope of this graph?

Write your answer in simplest form. If the denominator is 1, no need to write the denominator.

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What is the y-intercept of this graph?

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Write the equation of this line in slope-intercept form.

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What is the rise?

Don't forget that if the line is going down, then write the rise as negative.

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What is the run?

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What is the slope?

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What is the y-intercept?

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Write the equation of this line in slope-intercept form.

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What is the rise?

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What is the run?

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What is the slope?

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What is the y-intercept?

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Write the equation of this line in slope-intercept form.

First, choose any two points from the table and calculate or the slope. Put this value into m.

Second, look for the y-intercept in the table.​ Put the y-coordinate into b.

Slope-intercept from Graphs

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Write the equation of the line going through these points in slope-intercept form.

Step 1: Using points (0,-1) and (1,2), find the slope. Follow the format of the example below:

m=5--1/2-3=-4

Do not put spaces or parentheses.

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Write the equation of the line going through these points in slope-intercept form.

Step 2: Write the y-intercept of the graph as an ordered pair.

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Write the equation of the line going through these points in slope-intercept form.

Step 3: Write the slope-intercept form of the graph.

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Write the equation of the line going through these points in slope-intercept form.

Step 1: Using points (0,1) and (1,4), find the slope.

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Write the equation of the line going through these points in slope-intercept form.

Step 2: Write the y-intercept.

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Write the equation of the line going through these points in slope-intercept form.

Step 3: Write the equation.

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Write the equation of the line going through these points in slope-intercept form.

Step 1: Using points (-2,3) and (2,1), find the slope.

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Write the equation of the line going through these points in slope-intercept form.

Step 2: Write the y-intercept.

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Write the equation of the line going through these points in slope-intercept form.

Step 3: Write the equation.

Step 1: Graph b.

Step 2: Move to the next point using m.

Step 3: Connect.​

Graphing Slope-intercept

Multiple Choice

Choose the graph that matches the equation below:

$$y=x+2$$  

Don't forget the m there is invisible 1. Or you can think of it as a fraction $$\frac{1}{1}$$  .

Multiple Choice

Choose the graph that matches the equation below:

$$y=-\frac{4}{5}x+4$$  

Multiple Choice

Choose the graph that matches the equation below:

$$y=x-2$$  

Multiple Choice

Choose the graph that matches the equation below:

$$y=2x-3$$  

Multiple Choice

Choose the graph that matches the equation below:

$$y=-4x+4$$  

Multiple Choice

Choose the graph that matches the equation below:

$$y=\frac{1}{2}x-1$$  

Multiple Choice

Choose the graph that matches the equation below:

$$y=\frac{1}{2}x$$  

Note: Don't panic - If you don't see b, that simply means b must be a 0, and that's why it's "invisible". In other words, the y-intercept would be (0,0).