How do you graph the lines using slope-intercept form #y = -5x#?

1 Answer
Aug 5, 2017

The graph of #y=-5x# looks like this:
graph{y=-5x [-10, 10, -5, 5]}


The slope-intercept form of a line is #y=mx+b#, where
#m# = slope , and
#b# = y-intercept

To graph a line, you need to draw two points and connect a line between them. In the case of using the slope-intercept form, you will be using a point (the y-intercept) and the slope (m) to find the next point.

In this question, we have #y=color(red)-color(red)5x#. You can see that this is already in the form #y=color(red)mx+b# and that our slope is #m=-5#.

Now we can look at the y-intercept. Since we are looking at where the line crosses the y-axis, we already know that x=0 at that point. b, the y-intercept is just 0 since the original equation does not have a value for b. This means that the line crosses the y-axis at the point where y=0, so at the point with coordinates (0,0).

This is where we start (at the point (0,0)). From there, we draw the next point using the slope. We know the slope is -5, and since slope=change in y/change in x, we can say that it is -5/1. This just means that we go 5 units up the y-axis and 1 unit left on the x-axis (since we have a negative sign) from the point y=0. This gives us a new point. Alternatively, we can go 5 units down the y-axis (since we have a negative sign) and 1 unit right. Now that we have two points, we connect them and we have our line. It looks like this:
graph{y=-5x [-10, 10, -5, 5]}

If you have a positive slope, you would either go up the y-axis and right on the x-axis, or down on the y-axis and left on the x-axis.