Question

Find the missing coordinate r?

Answer 1

`r=-4`

Explanation:

`"slope" = (Deltay)/(Deltax)=(r-(-6))/(11-7)=(r+6)/4`

and, we are told that
`"slope" = 1/2`

Therefore
`color(white)("XXX")(r+6)/4=1/2`

...after multiplying both sides by `4`
`color(white)("XXX")r+6=2`

...then subtracting `6` from both sides
`color(white)("XXX")r=-4`

Answer 2

`-4=r`

Explanation:

Remember the formula for the slope `m`.

`(y_2-y_1)/(x_2-x_1)`

Even though your choice for `x_2` and `x_1` does not matter in this formula, it will prove significant when you start learning about things like vector, where direction matters. (It's fine if you didn't understand what I just said)

We name `(7,6)` as `(x_1,y_1)` and `(11,r)` as `(x_2,y_2)`

We can now plug these value into the formula.

`m=(y_2-y_1)/(x_2-x_1)`

`1/2=(r-(-6))/(11-7)`

`1/2=(r+6)/4` Cross multiply.

`4=2(r+6)` Distribute

`4=2r+12` Subtract `12` for both sides

`-8=2r` Divide both sides by `2`.

`-4=r`