How do you graph #y=1/3x-5# using the slope and intercept?

1 Answer
Mar 3, 2018

Using the slope-intercept form of the equation gives you

⁕ a value at #b# that tells you where to start

⁕ a value at #m# that tells you what to do to find the slope of the line.


The slope-intercept form of the equation is the easiest to graph because you can read the process right from the equation.

First you need a place to start

The equation gives you one point that is automatically on the line. That point is the y intercept, the value at b.

So to start, put the tip of the pencil on the y intercept.
In this case, that is #(0,#-#5)#

Now you count out the steps for the slope.

The slope is always a fraction.

Sometimes the value for slope doesn't even really look like a fraction.
The slope might be a whole number whose denominator is #1#, which may not even be written because it is understood.

But in this case, the slope is obviously the fraction #(1)/(3)#

Slope is described as "rise over run"
⁕ The numerator is how high you rise up the y axis.
⁕ The denominator is how far you run along the x axis.

1) So in this case, starting at #(0,"-"5)#, rise one step up the #y# axis.
Now you are at #(0,"-"4)#

2) From there, run along #3# steps parallel to the #x# axis
Now you are at #(3,"-"4)#

3) Draw a small dot at this new point.

4) Draw a line through the #y# intercept and this new point

graph{y = 1/3x - 5 [-7.67, 12.33, -8.6, 1.4]}