Answer:
The x intercept of the line is x = 9.
Step-by-step explanation:
The equation of a line has the following format:
[tex]y = ax + b[/tex]
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
[tex]y = ax + b[/tex]
[tex]-48 = -15a + b[/tex]
(-9,-32)
This means that when x = -9 y = -32. So
[tex]y = ax + b[/tex]
[tex]-32 = -9a + b[/tex]
From the first equation, we have that:
[tex]b = 15a - 48[/tex]
Then
[tex]-32 = -9a + b[/tex]
[tex]-9a + 15a - 48 = -32[/tex]
[tex]6a = 16[/tex]
[tex]a = \frac{8}{3}[/tex]
[tex]b = 15a - 48 = \frac{15*8}{3} - 48 = \frac{15*8 - 48*3}{3} = -24[/tex]
Then
[tex]y = \frac{8x}{3} - 24[/tex]
What is the x intercept of the line?
The x intercept is x when y = 0. Then
[tex]\frac{8x}{3} - 24 = 0[/tex]
[tex]\frac{8x}{3} = 24[/tex]
[tex]8x = 24*3[/tex]
[tex]x = 9[/tex]
The x intercept of the line is x = 9.
