Both equations are written in slope intercept form: `y = mx + b.`

In the equation `y = 1/4x - 2, ` `1/4` , is the slope and -2 is the y-intercept.

Plot (-2) on the y-axis and use slope (rate of change) to find next point. Since slope is 1/4, from the y-intercept, count up 1, right 4 and graph line. (See black line on graph)

In the equation `y = -2x` , -2 is the slope and 0 is y-intercept. Plot y-intercept, then count down 2 right 1 for slope. Draw line. (See red line on graph).See graphs below.

(I) `y=1/4x-2`

Since the equation is in slope-intercept form, use the y-intercept and the slope to graph it.

The y-intercept of this equation is (0,-2). And its slope is 1/4.

Since the slope is `1/4` , to get the next point, move (0,-2) one unit up and 4 units to the right. Hence, the next point is (4, -1). And to get the point next to this, move (4,-1) one unit up and 4 units to the right. So, the next point is (8,0).

Then, connect these three points and extend the line on both ends.

Hence, the graph of `y=1/4x-2` is the blue line below.

(II) y=`-2x`

Again, this equation is in slope-intercept form. So to graph this, use its y-intercept and slope.

The y-intercept of this equation is (0,0) and its slope is -2. For clarity, express the slope as a fraction. Its fraction form is `-2/1` .

So, plot the point (0,0). Then, refer to the slope `-2/1` to determine the next point.

To get the next point, move (0,0) two units down and one unit to the right. Hence, the next point is (1,-2). To get the point next to this, move (1,-2) two units down and one unit to the right. Hence, the next point is (2, -4).

After plotting the three points, connect them and extend the line on both ends.

Hence, the graph of `y=-2x` is the red line below.

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now