Question

A line passes through `(5 ,8 )` and `(2 ,9 )`. A second line passes through `(3 ,5 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

There are many answers based on the selected `x` value.
One answer is `(6, 4)`

Explanation:

Given: two parallel lines: `"line"_1 (5, 8), (2, 9); " " "line"_2 (3,5)`

Find the slope of `"line"_1`:
`m = (y_2 - y_1)/(x_2 - x_1) = (9 - 8)/(2 - 5) = 1/-3 = -1/3`

Parallel lines have the same slope.

Find the equation of the second line using the given point: `y - y_1 = m(x - x_1)`

`y - 5 = -1/3 (x - 3)`

Simplify by using distribution and adding `5` to both sides:
`y - 5 = -1/3x + (-1/3)(-3/1)`

`y - 5 = -1/3x + 1`

`y = -1/3x + 6`

To get another point, just plug in any `x` value.

Let `x = 6; y = -1/3 * 6/1 + 6 = -2 + 6 = 4; " "(6, 4)`