Question

A line passes through `(4 ,3 )` and `(7 ,1 )`. A second line passes through `(1 ,8 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

Find the slope of the first line, then apply it to the point of the second line to find `(1+3,8-2)=(4,6)`

Explanation:

We can solve this by finding the slope of the first line, then applying that slope to the point of the second line.

The first line passes through points `(4,3) and (7,1)`. Let's determine the slope.

The equation of slope is `m=(y_2-y_1)/(x_2-x_1)`. Let's plug in our points into this equation:

`m=(1-3)/(7-4)=-2/3`

We can now apply this slope to point `(1,8)`. I'll move 3 to the right on the x axis and 2 down on the y:

`(1+3,8-2)=(4,6)`