Question

Which point on the x-axis lies on the line that passes through point C and is parallel to line AB?

Answer 1

It is ( 2,0 ) 
It took me a while because I didn't went to school for 2 months.

Answer 2

Step 1

Find the slope of the line AB

Let

$A(-4,0)\ B(2,-3)$

we know that

The slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{-3-0}{2+4}$

$m=\frac{-3}{6}$

$m=-\frac{1}{2}$

Step 2

Find the equation of the line

we know that

If two lines are parallel, then their slopes are the same

so

$m1=m2$

The equation of the line into slope-point form is equal to

$y-y1=m(x-x1)$

we have

$m=-\frac{1}{2}$

point $C(-2,2)$

substitute

$y-2=-\frac{1}{2}(x+2)$

$y=-\frac{1}{2}x+1$

Step 3

Find the point on the x-axis that  lies on the line

the equation of the line is $y=-\frac{1}{2}x+1$

we know that

if the point lies on the x-axis

then

the y-coordinate of the point is equal to zero

so

For $y=0$

find the x-value

$0=-\frac{1}{2}x+1$

$\frac{1}{2}x=1$

$x=2$

therefore

the answer is

the point is $(2,0)$