Exercise 3 Page 194

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

y = m x + b

In this form,

m

is the slope of the line 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

The

y -

intercept is the

y -

value where the line crosses the

y -

axis.

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

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. Doing so, we will be able to identify the slope $m$ using the $rise$ and $run$ of the graph.

Here, we have used the given

(- 2, 4)

as our other point. Traveling to this point from the

y -

intercept requires that we move

2

steps horizontally in the negative direction and

4

steps vertically in the positive direction.

\frac{rise}{run} = \frac{4}{- 2} \Leftrightarrow m = - 2

Writing the Equation

Now that we have the slope and the

y -

intercept, we can form our final equation.

y = m x + b ⇓ y = - 2 x + 0

Therefore, the equation of the line for the given graph is

y = - 2 x .

Exercise 3 Page 194

Finding the y-intercept

Finding the Slope

Writing the Equation

Finding the $y -$ intercept