Question

How do you find the value of r such the points (6,-2), (r,-6) has slope m=4?

Answer 1

By starting with the slope formula `m=(y_2-y_1)/(x_2-x_1)`, plugging in the known values, and solving for the one remaining.

`r=5`.

Explanation:

The slope `m` of a line that connects point `(x_1, y_1)` and point `(x_2, y_2)` is "how fast `y` changes relative to how fast `x` changes". As a formula, this is

`m=(Delta y)/(Delta x)=(y_2-y_1)/(x_2-x_1)`

We are given

`(x_1,y_1) = (6, "–"2)`,
`(x_2,y_2) = (r, "–"6)`, and
`m=4`.

All we need to do is plug these into our slope formula and solve for `r`:

`color(white)=>m=(y_2-y_1)/(x_2-x_1)`

`=>4=("–"6-("–"2))/(r-6)`

`=>4(r-6)="–"6+2`

`=>r-6=("–"4)/4`

`=>r="–"1+6`

`=>r=5`

So in order for the line connecting `(6,"–2")` and `(r,"–6")` to have a slope of `4`, we need `r=5`.