Question

What is the distance between the two y-intercepts of these equations?

2x + 3y = -12
5x + 2y = 8​

Answer 1

Answer: 8 units

Explanation:

First, we must find the y-intercepts. To do this, we will transform both equations into slope-intercept form.

2x + 3y = -12

3y = 2x - 12

y =
`(2)/(3)`x - 4

5x + 2y = 8​

2y = 5x + 8

y =
`(5)/(2)`x + 4

These equations have y-intercepts of positive 4 and negative four. Since they are both on the y-axis as y-intercepts, we can find the distance between these two points with the following equation. Let x be equal to the distance between them.

|4| + |-4| = x

4 + 4 = x

x = 8

I have also graphed the two equations, see attached.