Question

A line passes through `(3 ,5 )` and `(6 ,8 )`. A second line passes through `(7 ,4 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

See explanation for a list of points, as well as how to find the list of points.

Explanation:

Since we have two parallel lines, the slopes are the same. So, our first step should be finding the slope of the first line.

The slope formula is:

`m=(y2-y1)/(x2-x1)`

So let's plug in values.

`m=(8-5)/(6-3)`

Now, simplify.

`m=3/3`

`m=1`

So the slopes of the line is 1, and since the lines are parallel, that is also the slope of the second line. Since the slope is 1, for every unit you go up in x value, you also go up one unit in y value. So here is a list of points that fall on the second line:

(8,5)

(9,6)

(10,7)

Additionally, you can go the other way: every unit you go down in x value, you go down a unit in y value. So here is a list of points going in the other direction:

(6,3)

(5,2)

(4,1)

Here are the intercepts if you are asked for them:

X-intercept: (3,0)

Y-intercept: (0, -3)