Question

What are the intercepts of `-x+3y=-3`?

Answer 1

The x-intercept is `(3,0)`.

The y-intercept is `(0,-1)`.

Explanation:

Given:

`-x+3y=-3` is a linear equation in standard form:

`Ax+By=C`.

X-intercept: value of `x` when `y=0`.

Substitute `0` for `y` and solve for `x`.

`-x+3(0)=-3`

`-x=-3`

Multiply both sides by `-1`.

`x=3`

The x-intercept is `(3,0)`.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Y-intercept: value of `y` when `x=0`

Substitute `0` for `x` and solve for `y`.

`0+3y=-3`

`3y=-3`

Divide both sides by `3`.

`(color(red)cancel(color(black)(3))^1y)/(color(red)cancel(color(black)(3))^1)=-color(red)cancel(color(black)(3))^1/color(red)cancel(color(black)(3))^1`

`y=-1`

The y-intercept is `(0,-1)`.

You can graph this equation by plotting the x- and y-intercepts and drawing a straight line through them.

graph{-x+3y=-3 [-11.25, 11.25, -5.625, 5.625]}