Question

How do you determine the value of 4 so that (5,r), (2,3) has slope 2?

Answer 1

It all depends on the formula slope `= (y_2-y_1)/(x_2-x_1)`

Explanation:

Here,

`"slope" = 2`

Using the formula, we get

`2 = (3-r)/(2-5)`

So ,

`3-r = -6`

`-r = -9`

Hence, the value of `r` is `9`.

Answer 2

r = 9

Explanation:

The formula for slope is
m = `(y - y_1)/(x - x_1)`

You have one unknown, r, the value of one of the y's, so write in the given values of everything else and solve for r.

Let `(5,r)` be assigned as `(x,y)`
Let (2,3) be assigned as `(x_1,y_1)`

m = `(y - y_1)/(x - x_1)`

2 = `(r - 3)/(5 - 2)`
Solve for `r`

1) Combine like terms
2 = `(r - 3)/(3)`

2) Clear the fraction by multiplying both sides by 3 and letting the denominator cancel
`6 = r - 3`

3) Add 3 to both sides to isolate `r`
`9 = r` <-- answer

Answer
`r = 9`
...........................

Check
Sub 9 back into the original equation in the place of `r` and see if `m` will still equal `2`

`2 = (r−3)/(5−2)`

1) Sub in 9 in the place of `r`
`2` should still equal `(9−3)/(5−2)`

2) Combine like terms
`2` should still equal `(6)/(3)`

3) `2` does equal `2`
Check!