Algebra Examples

(- 3, y)

$(- 3, y)$ and

(1, - 7)

$(1, - 7)$ ,

m = - 4

$m = - 4$

Step 1

Slope

m

$m$ is equal to the change in

y

$y$ over the change in

x

$x$ .

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

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

Step 2

Substitute in the values of the known parameters.

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

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

Step 3

Solve for

y

$y$ .

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Step 3.1

Rewrite the equation as

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

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

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

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

Step 3.2

Multiply both sides by

1 - (- 3)

$1 - (- 3)$ .

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

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

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Step 3.3.1.1.1

Cancel the common factor of

1 - - 3

$1 - - 3$ .

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Step 3.3.1.1.1.1

Multiply by

1

$1$ .

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

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

Step 3.3.1.1.1.2

Multiply by

1

$1$ .

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

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

Step 3.3.1.1.1.3

Rewrite the expression.

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

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

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

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

Step 3.3.1.1.2

Reorder

- 7

$- 7$ and

- y

$- y$ .

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

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

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

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

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

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

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify

- 4 (1 - (- 3))

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

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Step 3.3.2.1.1

Multiply

- 1

$- 1$ by

- 3

$- 3$ .

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

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

Step 3.3.2.1.2

Add

1

$1$ and

3

$3$ .

- y - 7 = - 4 \cdot 4

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

Step 3.3.2.1.3

Multiply

- 4

$- 4$ by

4

$4$ .

- y - 7 = - 16

$- y - 7 = - 16$

- y - 7 = - 16

$- y - 7 = - 16$

- y - 7 = - 16

$- y - 7 = - 16$

- y - 7 = - 16

$- y - 7 = - 16$

Step 3.4

Solve for

y

$y$ .

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Step 3.4.1

Move all terms not containing

y

$y$ to the right side of the equation.

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Step 3.4.1.1

Add

7

$7$ to both sides of the equation.

- y = - 16 + 7

$- y = - 16 + 7$

Step 3.4.1.2

Add

- 16

$- 16$ and

7

$7$ .

- y = - 9

$- y = - 9$

- y = - 9

$- y = - 9$

Step 3.4.2

Divide each term in

- y = - 9

$- y = - 9$ by

- 1

$- 1$ and simplify.

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Step 3.4.2.1

Divide each term in

- y = - 9

$- y = - 9$ by

- 1

$- 1$ .

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

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

Step 3.4.2.2.2

Divide

y

$y$ by

1

$1$ .

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

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

y = \frac{- 9}{- 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

$- 9$ by

- 1

$- 1$ .

y = 9

$y = 9$

y = 9

$y = 9$

y = 9

$y = 9$

y = 9

$y = 9$

y = 9

$y = 9$