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

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.

#### 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 $\frac{1}{3}$

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 $\left(0 , \text{-} 5\right)$, rise one step up the $y$ axis.
Now you are at $\left(0 , \text{-} 4\right)$

2) From there, run along $3$ steps parallel to the $x$ axis
Now you are at $\left(3 , \text{-} 4\right)$

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]}