Question

A line passes through `(2 ,8 )` and `( 1, 5 )`. A second line passes through `( 6, 1 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

`color(violet)("One other point on the second line is " (7,4)`

Explanation:

`"Slope of line 1 " = m = (y_2 - y_1) / (x_2 - x_1) = (5-8) / (1-2) = 3`


As `2^(nd)` line is parallel to the first line, slope of second line also `3`

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

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

`3x - y = 17`

Let y = 4. Then x = 7#

`color(violet)("One other point on the second line is " (7,4)`