Answer:
The x-intercept is the point (22,0)
Step-by-step explanation:
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take the points
(-38,40) and (-23,30)
substitute the given values
[tex]m=\frac{30-40}{-23+38}[/tex]
[tex]m=\frac{-10}{15}[/tex]
[tex]m=-\frac{2}{3}[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{2}{3}[/tex]
[tex]point\ (-8,20)[/tex]
substitute
[tex]y-20=-\frac{2}{3}(x+8)[/tex]
step 3
Find the x-intercept
Remember that the x-intercept is the value of x when the value of y is equal to zero
so
For y=0
[tex]0-20=-\frac{2}{3}(x+8)[/tex]
solve for x
[tex]-20=-\frac{2}{3}x-\frac{16}{3}[/tex]
Multiply by 3 both sides
[tex]-60=-2x-16[/tex]
[tex]2x=60-16\\2x=44\\x=22[/tex]
therefore
The x-intercept is the point (22,0)
