Question

A line passes through `(2 ,8 )` and `( 7, 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

`(11, -2)` is a point through which the second line might pass.

Explanation:

Parallel lines have equal slopes, so the first step is to find the slope of the line which passes through (`2, 8)` and `(7, 5)` using the slope formula. The formula for slope, `m`, is:
`m = (y_2 - y_1)/(x_2 - x_1)`

Substitute the known coordinates:
`m = (5 -8)/(7 - 2)`
`m = (-3)/5`

Remember that slope is "rise over run", so the numerator of the slope can be added to the `y`-coordinate of the known point and the denominator of the slope can be added to the `x`-coordinate of the known point to find another point on the other line.

`(6 + 5, 1 + -3)`
`(11, -2)`

So, `(11, -2)` is a point through which the second line might pass.

Answer 2

`color(green)(""(11,-2))`

Explanation:

Slope of line through `(2,8)` and `(7,5)`
`color(white)("XXX")m=(Deltay)/(Deltax)= (8-5)/(2-7)=-3/5`

This means that a change `Deltax=5` would correspond to a change `Deltay=-3`

So `(6+Deltax,1+Deltay)` would be a point `(11,-2)`