Solve for r (12,10) , (-2,r) , m=-4

$(12, 10)$ , $(- 2, r)$ , $m = - 4$

Slope $m$ is equal to the change in $y$ over the change in $x$ .

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute in the values of the known parameters.

$- 4 = \frac{r - (10)}{- 2 - (12)}$

Solve for $r$ .

Rewrite the equation as $\frac{r - (10)}{- 2 - (12)} = - 4$ .

$\frac{r - (10)}{- 2 - (12)} = - 4$

Multiply both sides of the equation by $- 2 - (12)$ .

$(- 2 - 1 \cdot 12) \frac{r - (10)}{- 2 - 1 \cdot 12} = (- 2 - (12)) \cdot - 4$

Simplify both sides of the equation.

Simplify the left side.

Simplify $(- 2 - 1 \cdot 12) \frac{r - (10)}{- 2 - 1 \cdot 12}$ .

Multiply $- 1$ by $10$ .

$(- 2 - 1 \cdot 12) \frac{r - 10}{- 2 - 1 \cdot 12} = (- 2 - (12)) \cdot - 4$

Simplify the denominator.

Multiply $- 1$ by $12$ .

$(- 2 - 1 \cdot 12) \frac{r - 10}{- 2 - 12} = (- 2 - (12)) \cdot - 4$

Subtract $12$ from $- 2$ .

$(- 2 - 1 \cdot 12) \frac{r - 10}{- 14} = (- 2 - (12)) \cdot - 4$

Simplify terms.

Multiply $- 1$ by $12$ .

$(- 2 - 12) \frac{r - 10}{- 14} = (- 2 - (12)) \cdot - 4$

Subtract $12$ from $- 2$ .

$- 14 \frac{r - 10}{- 14} = (- 2 - (12)) \cdot - 4$

Cancel the common factor of $14$ .

Factor $14$ out of $- 14$ .

$14 (- 1) \frac{r - 10}{- 14} = (- 2 - (12)) \cdot - 4$

Factor $14$ out of $- 14$ .

$14 \cdot - 1 \frac{r - 10}{14 \cdot - 1} = (- 2 - (12)) \cdot - 4$

Cancel the common factor.

$14 \cdot - 1 \frac{r - 10}{14 \cdot - 1} = (- 2 - (12)) \cdot - 4$

Rewrite the expression.

$- 1 \frac{r - 10}{- 1} = (- 2 - (12)) \cdot - 4$

Simplify the expression.

Move the negative one from the denominator of $\frac{r - 10}{- 1}$ .

$- 1 (- 1 \cdot (r - 10)) = (- 2 - (12)) \cdot - 4$

Rewrite $- 1 \cdot (r - 10)$ as $- (r - 10)$ .

$- 1 (- (r - 10)) = (- 2 - (12)) \cdot - 4$

Apply the distributive property.

$- 1 (- r - - 10) = (- 2 - (12)) \cdot - 4$

Multiply $- 1$ by $- 10$ .

$- 1 (- r + 10) = (- 2 - (12)) \cdot - 4$

Apply the distributive property.

$- 1 (- r) - 1 \cdot 10 = (- 2 - (12)) \cdot - 4$

Multiply $- 1 (- r)$ .

Multiply $- 1$ by $- 1$ .

$1 r - 1 \cdot 10 = (- 2 - (12)) \cdot - 4$

Multiply $r$ by $1$ .

$r - 1 \cdot 10 = (- 2 - (12)) \cdot - 4$

Multiply $- 1$ by $10$ .

$r - 10 = (- 2 - (12)) \cdot - 4$

Simplify the right side.

Simplify $(- 2 - (12)) \cdot - 4$ .

Multiply $- 1$ by $12$ .

$r - 10 = (- 2 - 12) \cdot - 4$

Subtract $12$ from $- 2$ .

$r - 10 = - 14 \cdot - 4$

Multiply $- 14$ by $- 4$ .

$r - 10 = 56$

Move all terms not containing $r$ to the right side of the equation.

Add $10$ to both sides of the equation.

$r = 56 + 10$

Add $56$ and $10$ .

$r = 66$

Solve for r (12,10) , (-2,r) , m=-4

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