Question

What are the intercepts of `5x+3y=13`?

Answer 1

The y-intercept is `13/3` or `(0, 13/3)`

The x-intercept is `13/5` or `(13/5, 0)`

Explanation:

Using the cover-up method we will solve for the y-intercept by eliminating the `x` term and solving for `y`;

`3y = 13`

`(3y)/color(red)(3) = 13/color(red)(3)`

`(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = 13/3`

`y = 13/3`

Therefore the y-intercept is `13/3` or `(0, 13/3)`

Using the cover-up method we will solve for the x-intercept by eliminating the `y` term and solving for `x`;

`5x = 13`

`(5x)/color(red)(5) = 13/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 13/5`

`x = 13/5`

Therefore the x-intercept is `13/5` or `(13/5, 0)`