Equations written in slope-intercept form follow a specific format, where

m

is the slope of the line and

b

is the

y -

intercept.

y = m x + b

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

y -

intercept.

Finding the $y -$ intercept

The

y -

intercept is the

y -

value where the line crosses the

y -

axis.

We can see that the function crosses the

y -

axis at

(0, - 1) .

This means that the value of

b

is

- 1 .

y = m x + (- 1) \Leftrightarrow y = m x - 1

Finding the Slope

To find the slope, we will trace along the line on the given graph until we find a lattice point. 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

x -

intercept at

(2, 0)

as our other point. Traveling to this point from the

y -

intercept requires that we move

1

step vertically in the positive direction, and

2

steps horizontally in the positive direction.

\frac{rise}{run} = \frac{1}{2} \Leftrightarrow m = \frac{1}{2}

Writing the Equation

Now that we have the slope and the

y -

intercept, we can form our final equation.

y = \frac{1}{2} x - 1

Finding the y-intercept

Finding the Slope

Writing the Equation

Finding the $y -$ intercept

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