Solve for r (r,-5) , (3,13) , m=8

$(r, - 5)$ , $(3, 13)$ , $m = 8$

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.

$8 = \frac{13 - (- 5)}{3 - (r)}$

Step 3

Solve for $r$ .

Rewrite the equation as $\frac{13 - (- 5)}{3 - (r)} = 8$ .

$\frac{13 - (- 5)}{3 - (r)} = 8$

Factor each term.

Multiply $- 1$ by $- 5$ .

$\frac{13 + 5}{3 - (r)} = 8$

Add $13$ and $5$ .

$\frac{18}{3 - (r)} = 8$

Multiply $- 1$ by $r$ .

$\frac{18}{3 - r} = 8$

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.

$3 - r, 1$

Remove parentheses.

$3 - r, 1$

The LCM of one and any expression is the expression.

$3 - r$

Multiply each term in $\frac{18}{3 - r} = 8$ by $3 - r$ to eliminate the fractions.

Multiply each term in $\frac{18}{3 - r} = 8$ by $3 - r$ .

$\frac{18}{3 - r} (3 - r) = 8 (3 - r)$

Simplify the left side.

Cancel the common factor of $3 - r$ .

Cancel the common factor.

$\frac{18}{3 - r} (3 - r) = 8 (3 - r)$

Rewrite the expression.

$18 = 8 (3 - r)$

Simplify the right side.

Apply the distributive property.

$18 = 8 \cdot 3 + 8 (- r)$

Multiply.

Multiply $8$ by $3$ .

$18 = 24 + 8 (- r)$

Multiply $- 1$ by $8$ .

$18 = 24 - 8 r$

Solve the equation.

Rewrite the equation as $24 - 8 r = 18$ .

$24 - 8 r = 18$

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

Subtract $24$ from both sides of the equation.

$- 8 r = 18 - 24$

Subtract $24$ from $18$ .

$- 8 r = - 6$

Divide each term in $- 8 r = - 6$ by $- 8$ and simplify.

Divide each term in $- 8 r = - 6$ by $- 8$ .

$\frac{- 8 r}{- 8} = \frac{- 6}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 r}{- 8} = \frac{- 6}{- 8}$

Divide $r$ by $1$ .

$r = \frac{- 6}{- 8}$

Simplify the right side.

Cancel the common factor of $- 6$ and $- 8$ .

Factor $- 2$ out of $- 6$ .

$r = \frac{- 2 (3)}{- 8}$

Cancel the common factors.

Factor $- 2$ out of $- 8$ .

$r = \frac{- 2 \cdot 3}{- 2 \cdot 4}$

Cancel the common factor.

$r = \frac{- 2 \cdot 3}{- 2 \cdot 4}$

Rewrite the expression.

$r = \frac{3}{4}$

Solve for r (r,-5) , (3,13) , m=8

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