Exercise 25 Page 482

Equations written in slope-intercept form follow a specific format. y= mx+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. rise/run=-3/1 ⇔ m= -3/1

Writing the Equation

Now that we have the slope and the y-intercept, we can form our final equation. y= mx+b y= -3x+2