Question

-3x+2y=6 Find the intercepts. Show your work.

Answer 1

The x-intercept is (-2,0)

The y-intercept is (0,3)

Explanation:

An x-intercept is the point when the graph crosses the x-axis. In other words, the y-coordinate of the x-intercept is 0 (since it lays on the x-axis). In other words, to solve for the x-intercept(s), plug in 0 for y and solve for x:

`-3x+2y=6\\-3x+2(0)=6\\-3x=6\\x=-2`

So, the x-intercept is (-2,0).

Likewise, the y-intercept is the point when the graph crosses the y-axis. Because it's on the y-axis, the x-coordinate value would be 0. Thus, to find the y-intercept, plug in 0 for x and solve for y:

`-3x+2y=6\\-3(0)+2y=6\\2y=6\\y=3`

Thus, the y-intercept is (0,3).