Solve for r (5,9) , (r,-3) , m=-4

$(5, 9)$ , $(r, - 3)$ , $m = - 4$

Step 1

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

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

Step 2

Substitute in the values of the known parameters.

$- 4 = \frac{- 3 - (9)}{r - (5)}$

Step 3

Solve for $r$ .

Rewrite the equation as $\frac{- 3 - (9)}{r - (5)} = - 4$ .

$\frac{- 3 - (9)}{r - (5)} = - 4$

Factor each term.

Multiply $- 1$ by $9$ .

$\frac{- 3 - 9}{r - (5)} = - 4$

Subtract $9$ from $- 3$ .

$\frac{- 12}{r - (5)} = - 4$

Multiply $- 1$ by $5$ .

$\frac{- 12}{r - 5} = - 4$

Move the negative in front of the fraction.

$- \frac{12}{r - 5} = - 4$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$r - 5, 1$

Remove parentheses.

$r - 5, 1$

The LCM of one and any expression is the expression.

$r - 5$

Multiply each term in $- \frac{12}{r - 5} = - 4$ by $r - 5$ to eliminate the fractions.

Multiply each term in $- \frac{12}{r - 5} = - 4$ by $r - 5$ .

$- \frac{12}{r - 5} (r - 5) = - 4 (r - 5)$

Simplify the left side.

Cancel the common factor of $r - 5$ .

Move the leading negative in $- \frac{12}{r - 5}$ into the numerator.

$\frac{- 12}{r - 5} (r - 5) = - 4 (r - 5)$

Cancel the common factor.

$\frac{- 12}{r - 5} (r - 5) = - 4 (r - 5)$

Rewrite the expression.

$- 12 = - 4 (r - 5)$

Simplify the right side.

Apply the distributive property.

$- 12 = - 4 r - 4 \cdot - 5$

Multiply $- 4$ by $- 5$ .

$- 12 = - 4 r + 20$

Solve the equation.

Rewrite the equation as $- 4 r + 20 = - 12$ .

$- 4 r + 20 = - 12$

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

Subtract $20$ from both sides of the equation.

$- 4 r = - 12 - 20$

Subtract $20$ from $- 12$ .

$- 4 r = - 32$

Divide each term in $- 4 r = - 32$ by $- 4$ and simplify.

Divide each term in $- 4 r = - 32$ by $- 4$ .

$\frac{- 4 r}{- 4} = \frac{- 32}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 r}{- 4} = \frac{- 32}{- 4}$

Divide $r$ by $1$ .

$r = \frac{- 32}{- 4}$

Simplify the right side.

Divide $- 32$ by $- 4$ .

$r = 8$

Solve for r (5,9) , (r,-3) , m=-4

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