Answer:
The x-intercept of the line is the point (12,0)
Step-by-step explanation:
step 1
Find the slope of the lime
Take the points
(22,36) and (32,72)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{72-36}{32-22}[/tex]
[tex]m=\frac{36}{10}[/tex]
[tex]m=3.6[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=3.6[/tex]
[tex]point (22,36)[/tex]
substitute
[tex]y-36=3.6(x-22)[/tex]
step 3
Find the x-intercept
we know that
The x-intercept of a line is the value of x when the value of y is equal to zero
so
For y=0
substitute in the equation and solve for x
[tex]0-36=3.6(x-22)[/tex]
[tex]0-36=3.6x-79.2[/tex]
[tex]3.6x=79.2-36[/tex]
[tex]3.6x=43.2[/tex]
[tex]x=12[/tex]
therefore
The x-intercept of the line is the point (12,0)
