Algebra Examples

$(- 3, y)$ and $(1, - 7)$ , $m = - 4$

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.

$- 4 = \frac{- 7 - (y)}{1 - (- 3)}$

Step 3

Solve for $y$ .

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Step 3.1

Rewrite the equation as $\frac{- 7 - (y)}{1 - (- 3)} = - 4$ .

$\frac{- 7 - (y)}{1 - (- 3)} = - 4$

Step 3.2

Multiply both sides by $1 - (- 3)$ .

$\frac{- 7 - (y)}{1 - (- 3)} (1 - (- 3)) = - 4 (1 - (- 3))$

Step 3.3

Simplify.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $\frac{- 7 - (y)}{1 - (- 3)} (1 - (- 3))$ .

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Step 3.3.1.1.1

Cancel the common factor of $1 - - 3$ .

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Step 3.3.1.1.1.1

Multiply by $1$ .

$\frac{- 7 - (y)}{(1 - (- 3)) \cdot 1} (1 - (- 3)) = - 4 (1 - (- 3))$

Step 3.3.1.1.1.2

Multiply by $1$ .

$\frac{- 7 - (y)}{(1 - (- 3)) \cdot 1} ((1 - (- 3)) \cdot 1) = - 4 (1 - (- 3))$

Step 3.3.1.1.1.3

Rewrite the expression.

$- 7 - (y) = - 4 (1 - (- 3))$

Step 3.3.1.1.2

Reorder $- 7$ and $- y$ .

$- y - 7 = - 4 (1 - (- 3))$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $- 4 (1 - (- 3))$ .

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Step 3.3.2.1.1

Multiply $- 1$ by $- 3$ .

$- y - 7 = - 4 (1 + 3)$

Step 3.3.2.1.2

Add $1$ and $3$ .

$- y - 7 = - 4 \cdot 4$

Step 3.3.2.1.3

Multiply $- 4$ by $4$ .

$- y - 7 = - 16$

Step 3.4

Solve for $y$ .

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Step 3.4.1

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

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Step 3.4.1.1

Add $7$ to both sides of the equation.

$- y = - 16 + 7$

Step 3.4.1.2

Add $- 16$ and $7$ .

$- y = - 9$

Step 3.4.2

Divide each term in $- y = - 9$ by $- 1$ and simplify.

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Step 3.4.2.1

Divide each term in $- y = - 9$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 9}{- 1}$

Step 3.4.2.2

Simplify the left side.

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Step 3.4.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 9}{- 1}$

Step 3.4.2.2.2

Divide $y$ by $1$ .

$y = \frac{- 9}{- 1}$

Step 3.4.2.3

Simplify the right side.

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Step 3.4.2.3.1

Divide $- 9$ by $- 1$ .

$y = 9$