Question

A line passes through `(2 ,8 )` and `(7 ,9 )`. A second line passes through `(3 ,6 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

`color(blue)("One other point on the second line is " (-2,5)`

Explanation:

`"Slope of line 1 " = m = (y_2 - y_1) / (x_2 - x_1) = (9-8) / (47-2) = 1/5`

![https://www.askiitians.com/iit-jee-straight-line/distance-between-two-parallel-lines/]()

As `2^(nd)` line is parallel to the first line, slope of second line also `1/5`

#"Equation of second line in point - slope form is "

`(y - 6) = 1/5 * (x - 3)`

`5y - 30 = x - 3`

`x - 5y = -27`

Let y = 5. Then x = -2#

graph{x/5 + 27/5 [-10, 10, -5, 5]}

`color(blue)("One other point on the second line is " (-2,5)`