Equations written in slope-intercept form follow a specific format.

y = m x + b

In this form,

m

is the slope and

b

is the

y -

intercept. We need to identify these values using the graph. Let's start with the

y -

intercept.

Finding the $y -$ intercept

Observe the given graph.

We can see that the function intercepts the $y -$ axis at $(0, 2) .$ This means that the value of $b$ is $2 .$

Finding the Slope

To find the slope, we will trace along the line on the given graph until we find a lattice point, which is a point that lies perfectly on the grid lines. In doing so, we will be able to identify the slope $m$ using the $rise$ and $run$ of the graph.

Here we've identified the

(1, - 1)

as our other point. Traveling to this point from the

y -

intercept requires that we move

1

step horizontally in the positive direction and

3

steps vertically in the negative direction.

\frac{rise}{run} = \frac{- 3}{1} \Leftrightarrow m = - \frac{3}{1}

Writing the Equation

Now that we have the slope and the

y -

intercept, we can form our final equation.

y = m x + b y = - 3 x + 2

Finding the y-intercept

Finding the Slope

Writing the Equation

Finding the $y -$ intercept

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