Question

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

Answer 1

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.

Explanation:

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]}