Question

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

Answer 1

Answer:

The x intercept of the line is x = 9.

Step-by-step 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

$-32 = -9a + b$

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

$6a = 16$

$a = \frac{8}{3}$

$b = 15a - 48 = \frac{15*8}{3} - 48 = \frac{15*8 - 48*3}{3} = -24$

Then

$y = \frac{8x}{3} - 24$

What is the x intercept of the line?

The x intercept is x when y = 0. Then

$\frac{8x}{3} - 24 = 0$

$\frac{8x}{3} = 24$

$8x = 24*3$

$x = 9$

The x intercept of the line is x = 9.