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

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Answer 1 · 2017-11-19T12:08:20

It all depends on the formula slope $= \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $= (y_2-y_1)/(x_2-x_1)$

Here,

$slope = 2$ $"slope" = 2$

Using the formula, we get

$2 = \frac{3 - r}{2 - 5}$ $2 = (3-r)/(2-5)$

So ,

$3 - r = - 6$ $3-r = -6$

$- r = - 9$ $-r = -9$

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

Answer 2 · 2017-11-19T12:09:03

r = 9

The formula for slope is
m = $\frac{y - y_{1}}{x - x_{1}}$ $(y - y_1)/(x - x_1)$

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 $(5, r)$ $(5,r)$ be assigned as $(x, y)$ $(x,y)$
Let (2,3) be assigned as $(x_{1}, y_{1})$ $(x_1,y_1)$

m = $\frac{y - y_{1}}{x - x_{1}}$ $(y - y_1)/(x - x_1)$

2 = $\frac{r - 3}{5 - 2}$ $(r - 3)/(5 - 2)$
Solve for $r$ $r$

1) Combine like terms
2 = $\frac{r - 3}{3}$ $(r - 3)/(3)$

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

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

Answer
$r = 9$ $r = 9$
...........................

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

$2 = \frac{r - 3}{5 - 2}$ $2 = (r−3)/(5−2)$

1) Sub in 9 in the place of $r$ $r$
$2$ $2$ should still equal $\frac{9 - 3}{5 - 2}$ $(9−3)/(5−2)$

2) Combine like terms
$2$ $2$ should still equal $\frac{6}{3}$ $(6)/(3)$

3) $2$ $2$ does equal $2$ $2$
Check!