Question

A line passes through `(2 ,8 )` and `( 3, 5 )`. A second line passes through `( 4, 8 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the slope of the first line. The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(5) - color(blue)(8))/(color(red)(3) - color(blue)(2)) = (-3)/1`

Because the two lines in the problem are parallel by definition they have the same slope.

A slope of `(-3)/1` means it has a rise of `-3` and a run of `1`. Or, in other words, for each `1` unit the line moves to the right on the `x` axis it moves down `3` units on the `y` axis.

We can find another point on the second line by adding `1` to the `x` coordinate and subtracting `3` from the `y` coordinate:

`(4 + 1, 8 - 3) => (5, 5)`