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
![m=\frac{y2-y1}{x2-x1}](/tpl/images/0368/7459/baca9.png)
substitute the values
![m=\frac{72-36}{32-22}](/tpl/images/0368/7459/9e2d6.png)
![m=\frac{36}{10}](/tpl/images/0368/7459/1d431.png)
![m=3.6](/tpl/images/0368/7459/4b5bd.png)
step 2
Find the equation of the line in point slope form
![y-y1=m(x-x1)](/tpl/images/0368/7459/11c10.png)
we have
![m=3.6](/tpl/images/0368/7459/4b5bd.png)
![point (22,36)](/tpl/images/0368/7459/79eb7.png)
substitute
![y-36=3.6(x-22)](/tpl/images/0368/7459/cc821.png)
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
![0-36=3.6(x-22)](/tpl/images/0368/7459/3dc49.png)
![0-36=3.6x-79.2](/tpl/images/0368/7459/df0ff.png)
![3.6x=79.2-36](/tpl/images/0368/7459/f78d9.png)
![3.6x=43.2](/tpl/images/0368/7459/8bbcb.png)
![x=12](/tpl/images/0368/7459/555c2.png)
therefore
The x-intercept of the line is the point (12,0)