Question

How do you find the x and y intercept of `8x − 3y = −21`?

Answer 1

See the entire solution process below:

Explanation:

To find the intercepts by substitution we must do the following:

y-intercept - substitute `0` for `x` and solve for `y`:

`8x - 3y = -21` becomes:

`(8 xx 0) - 3y = -21`

`0 - 3y = -21`

`-3y = -21`

`(-3y)/color(red)(-3) = (-21)/color(red)(-3)`

`(color(red)(cancel(color(black)(-3)))y)/cancel(color(red)(-3)) = 7`

`y = 7`

The y-intercept is `7` or `(0, 7)`

x-intercept - substitute `0` for `y` and solve for `x`:

`8x - 3y = -21` becomes:

`8x - (3 xx 0) = -21`

`8x - 0 = -21`

`8x = -21`

`(8x)/color(red)(8) = (-21)/color(red)(8)`

`(color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8)) = -21/8`

`x = -21/8`

The x-intercept is `-21/8` or `(-21/8, 0)`