Question

A line passes through `(2 ,3 )` and `( 6, 2 )`. A second line passes through `( 7, 4 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

Any set of points you put into that equation, should be parallel to the first line.

Explanation:

If two lines are parallel to each other, then they have the same slope. To find the slope of the first line, use point slope formula: `m = (y_2 - y_1)/(x_2 - x_1)` where `m` is the slope

`(2,3) and (6,2)` corresponds to `(x_1, y_1) and (x_2,y_2)`

Plug the numbers into the formula

`m= (2-3)/(6-2) = -1/4`

So, the slope is `-1/4`

Next, find the equation of the second line using this form:
`y=mx+b`, where `m` is the slope, which is `-1/4`

`y=-1/4x+b`

Now, to find `b`, which is the y-intercept, plug in the coordinates `(7,4)` into the y and x intercepts

`4=-1/4(7) +b`
`4=-7/4+b`
`23/4=b`

So, the equation should look like `y=-1/4x + 23/4`

Any set of points you put into that equation, should be parallel to the first line.

For example, if you put 0 in for x and solve, your y would be `23/4` so the points would be `(0,23/4)`