Question

How do you find slope and intercepts to graph `y=-2/3x - 1`?

Answer 1

The slope is `m=-2/3`, and the y- intercept is -1. The x-intercept is at `-3/2`.

Explanation:

This equation is written in slope-intercept form, which is `y = mx+b`, where m is the slope, and b is the y-intercept. The slope is the constant or number multiplied by the variable, x, which in this case is -2/3.

In order to find the intercepts, all you have to do is set the according variable equal to 0. For lines given in slope-intercept, this step is not needed, since the y-intercept is explicitly stated, but it is important to understand why that point is chosen.

For y-intercepts, the x-value is equal to 0, since we are trying to find the point at which the line crosses the y-axis.

For x-intercepts, the y-value is equal to 0, since we are trying to find the point at which the line crosses the x-axis. X-intercepts are a bit trickier, because you have to set the whole equation equal to 0 (since y = 0), and solve for x.

I found the x-int by doing the following:
I set y equal to 0: `y = -2/3x - 1 = 0`
I added both sides by 1: `-2/3x = 1`
I multiplied both sides by the reciprocal of -2/3, which is -3/2:
`x = -3/2`