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

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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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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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).