Question

What is the x intercept of the line? (-21,-64) (-15,-48) (-9,-32)

Answer 1

The x intercept of the line is x = 9.

Explanation:

The equation of a line has the following format:

`y = ax + b`

In this question, we have three points. We can take two of them to build the equation.

(-15,-48)

This means that when x = -15 y = -48. So

`y = ax + b`

`-48 = -15a + b`

(-9,-32)

This means that when x = -9 y = -32. So

`y = ax + b`

`-32 = -9a + b`

From the first equation, we have that:

`b = 15a - 48`

Then

`-32 = -9a + b`

`-9a + 15a - 48 = -32`

`6a = 16`

`a = (8)/(3)`

`b = 15a - 48 = (15*8)/(3) - 48 = (15*8 - 48*3)/(3) = -24`

Then

`y = (8x)/(3) - 24`

What is the x intercept of the line?

The x intercept is x when y = 0. Then

`(8x)/(3) - 24 = 0`

`(8x)/(3) = 24`

`8x = 24*3`

`x = 9`

The x intercept of the line is x = 9.