Question

Find a if the point (3,a) is on the line that passes through (-2,7) and (5,-3).

Answer 1

Your first step is to find the slope of the line. You can find that using the formula
`(y_(2)-y_(1))/(x_(2)-x_(1))`. Plug the x- and y- values from the coordinate pairs into the formula.


`(y_(2)-y_(1))/(x_(2)-x_(1))` Plug in the coordinates

`(-3 - 7)/(5 - (-2))` Cancel out the double negative

`(-3 - 7)/(5 + 2)` Add and subtract

`(-10)/(7)`

Next, you can use the same formula to find a by setting it against the slope you just found.

slope =
`(y_(2) - y_(1))/(x_(2) - x_(1))` Plug in the values

`(-10)/(7)` =
`(7 - a)/(-2 - 3)` Subtract

`(-10)/(7)` =
`(7 - a)/(-5)` Multiply both sides by 7
-10 =
`(7(7 - a))/(-5)` Use the Distributive Property
-10 =
`(49 -7a)/(-5)` Multiply both sides by -5
50 = 49 - 7a Subtract 49 from both sides
1 = -7a Divide both sides by -7

`-(1)/(7)` = a Switch the sides to make it easier to read
a =
`-(1)/(7)`