Algebra Examples

$(- 3, - 4)$ and $(- 5, y)$ , $m = - \frac{9}{2}$

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.

$- \frac{9}{2} = \frac{y - (- 4)}{- 5 - (- 3)}$

Step 3

Solve for $y$ .

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Step 3.1

Rewrite the equation as $\frac{y - (- 4)}{- 5 - (- 3)} = - \frac{9}{2}$ .

$\frac{y - (- 4)}{- 5 - (- 3)} = - \frac{9}{2}$

Step 3.2

Multiply both sides of the equation by $- 5 - (- 3)$ .

$(- 5 - - 3) \frac{y - (- 4)}{- 5 - - 3} = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $(- 5 - - 3) \frac{y - (- 4)}{- 5 - - 3}$ .

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Step 3.3.1.1.1

Multiply $- 1$ by $- 4$ .

$(- 5 - - 3) \frac{y + 4}{- 5 - - 3} = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.2

Simplify the denominator.

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Step 3.3.1.1.2.1

Multiply $- 1$ by $- 3$ .

$(- 5 - - 3) \frac{y + 4}{- 5 + 3} = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.2.2

Add $- 5$ and $3$ .

$(- 5 - - 3) \frac{y + 4}{- 2} = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.3

Simplify terms.

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Step 3.3.1.1.3.1

Multiply $- 1$ by $- 3$ .

$(- 5 + 3) \frac{y + 4}{- 2} = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.3.2

Add $- 5$ and $3$ .

$- 2 \frac{y + 4}{- 2} = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.3.3

Cancel the common factor of $2$ .

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Step 3.3.1.1.3.3.1

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{y + 4}{- 2} = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.3.3.2

Factor $2$ out of $- 2$ .

$2 \cdot - 1 \frac{y + 4}{2 \cdot - 1} = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.3.3.3

Cancel the common factor.

$2 \cdot - 1 \frac{y + 4}{2 \cdot - 1} = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.3.3.4

Rewrite the expression.

$- 1 \frac{y + 4}{- 1} = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.3.4

Simplify the expression.

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Step 3.3.1.1.3.4.1

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

$- 1 (- 1 \cdot (y + 4)) = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.3.4.2

Rewrite $- 1 \cdot (y + 4)$ as $- (y + 4)$ .

$- 1 (- (y + 4)) = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.3.5

Apply the distributive property.

$- 1 (- y - 1 \cdot 4) = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.3.6

Multiply $- 1$ by $4$ .

$- 1 (- y - 4) = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.3.7

Apply the distributive property.

$- 1 (- y) - 1 \cdot - 4 = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.4

Multiply $- 1 (- y)$ .

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Step 3.3.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 y - 1 \cdot - 4 = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.4.2

Multiply $y$ by $1$ .

$y - 1 \cdot - 4 = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.1.1.5

Multiply $- 1$ by $- 4$ .

$y + 4 = (- 5 - (- 3)) (- \frac{9}{2})$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $(- 5 - (- 3)) (- \frac{9}{2})$ .

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Step 3.3.2.1.1

Simplify the expression.

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Step 3.3.2.1.1.1

Multiply $- 1$ by $- 3$ .

$y + 4 = (- 5 + 3) (- \frac{9}{2})$

Step 3.3.2.1.1.2

Add $- 5$ and $3$ .

$y + 4 = - 2 (- \frac{9}{2})$

Step 3.3.2.1.2

Cancel the common factor of $2$ .

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Step 3.3.2.1.2.1

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$y + 4 = - 2 (\frac{- 9}{2})$

Step 3.3.2.1.2.2

Factor $2$ out of $- 2$ .

$y + 4 = 2 (- 1) \frac{- 9}{2}$

Step 3.3.2.1.2.3

Cancel the common factor.

$y + 4 = 2 \cdot - 1 \frac{- 9}{2}$

Step 3.3.2.1.2.4

Rewrite the expression.

$y + 4 = - 1 \cdot - 9$

Step 3.3.2.1.3

Multiply $- 1$ by $- 9$ .

$y + 4 = 9$

Step 3.4

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

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Step 3.4.1

Subtract $4$ from both sides of the equation.

$y = 9 - 4$

Step 3.4.2

Subtract $4$ from $9$ .

$y = 5$