Algebra Examples

$(- 2, 8)$ , $(r, 4)$ , $m = - \frac{1}{2}$

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.

$- \frac{1}{2} = \frac{4 - (8)}{r - (- 2)}$

Step 3

Solve for $r$ .

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Step 3.1

Rewrite the equation as $\frac{4 - (8)}{r - (- 2)} = - \frac{1}{2}$ .

$\frac{4 - (8)}{r - (- 2)} = - \frac{1}{2}$

Step 3.2

Simplify both sides.

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Step 3.2.1

Simplify the numerator.

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Step 3.2.1.1

Multiply $- 1$ by $8$ .

$\frac{4 - 8}{r - (- 2)} = - \frac{1}{2}$

Step 3.2.1.2

Subtract $8$ from $4$ .

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

Step 3.2.2

Multiply $- 1$ by $- 2$ .

$\frac{- 4}{r + 2} = - \frac{1}{2}$

Step 3.2.3

Move the negative in front of the fraction.

$- \frac{4}{r + 2} = - \frac{1}{2}$

Step 3.3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

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

Step 3.4

Solve the equation for $r$ .

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Step 3.4.1

Rewrite the equation as $(r + 2) \cdot - 1 = - 4 \cdot 2$ .

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

Step 3.4.2

Divide each term in $(r + 2) \cdot - 1 = - 4 \cdot 2$ by $- 1$ and simplify.

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Step 3.4.2.1

Divide each term in $(r + 2) \cdot - 1 = - 4 \cdot 2$ by $- 1$ .

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

Step 3.4.2.2

Simplify the left side.

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Step 3.4.2.2.1

Simplify by multiplying through.

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Step 3.4.2.2.1.1

Move the negative one from the denominator of $\frac{(r + 2) \cdot - 1}{- 1}$ .

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

Step 3.4.2.2.1.2

Rewrite $- 1 \cdot ((r + 2) \cdot - 1)$ as $- ((r + 2) \cdot - 1)$ .

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

Step 3.4.2.2.1.3

Apply the distributive property.

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

Step 3.4.2.2.1.4

Simplify the expression.

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Step 3.4.2.2.1.4.1

Move $- 1$ to the left of $r$ .

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

Step 3.4.2.2.1.4.2

Multiply $2$ by $- 1$ .

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

Step 3.4.2.2.2

Rewrite $- 1 r$ as $- r$ .

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

Step 3.4.2.2.3

Apply the distributive property.

$- - r - - 2 = \frac{- 4 \cdot 2}{- 1}$

Step 3.4.2.2.4

Multiply $- - r$ .

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Step 3.4.2.2.4.1

Multiply $- 1$ by $- 1$ .

$1 r - - 2 = \frac{- 4 \cdot 2}{- 1}$

Step 3.4.2.2.4.2

Multiply $r$ by $1$ .

$r - - 2 = \frac{- 4 \cdot 2}{- 1}$

Step 3.4.2.2.5

Multiply $- 1$ by $- 2$ .

$r + 2 = \frac{- 4 \cdot 2}{- 1}$

Step 3.4.2.3

Simplify the right side.

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Step 3.4.2.3.1

Move the negative one from the denominator of $\frac{- 4 \cdot 2}{- 1}$ .

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

Step 3.4.2.3.2

Rewrite $- 1 \cdot (- 4 \cdot 2)$ as $- (- 4 \cdot 2)$ .

$r + 2 = - (- 4 \cdot 2)$

Step 3.4.2.3.3

Multiply $- (- 4 \cdot 2)$ .

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Step 3.4.2.3.3.1

Multiply $- 4$ by $2$ .

$r + 2 = - - 8$

Step 3.4.2.3.3.2

Multiply $- 1$ by $- 8$ .

$r + 2 = 8$

Step 3.4.3

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

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Step 3.4.3.1

Subtract $2$ from both sides of the equation.

$r = 8 - 2$

Step 3.4.3.2

Subtract $2$ from $8$ .

$r = 6$