Algebra Examples

$(- 4, 8)$ , $(0, 0)$

Step 1

Find the slope of the line between $(- 4, 8)$ and $(0, 0)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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Step 1.1

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

Step 1.2

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

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

Step 1.3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{0 - (8)}{0 - (- 4)}$

Step 1.4

Simplify.

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Step 1.4.1

Reduce the expression by cancelling the common factors.

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Step 1.4.1.1

Cancel the common factor of $0 - (8)$ and $0 - (- 4)$ .

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Step 1.4.1.1.1

Rewrite $0$ as $- 1 (0)$ .

$m = \frac{- 1 \cdot 0 - (8)}{0 - (- 4)}$

Step 1.4.1.1.2

Factor $- 1$ out of $- 1 (0) - (8)$ .

$m = \frac{- 1 (0 + 8)}{0 - (- 4)}$

Step 1.4.1.1.3

Reorder terms.

$m = \frac{- 1 (0 + 8)}{0 - 4 \cdot - 1}$

Step 1.4.1.1.4

Factor $4$ out of $- 1 (0 + 8)$ .

$m = \frac{4 (- 1 (0 + 2))}{0 - 4 \cdot - 1}$

Step 1.4.1.1.5

Cancel the common factors.

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Step 1.4.1.1.5.1

Factor $4$ out of $0$ .

$m = \frac{4 (- 1 (0 + 2))}{4 (0) - 4 \cdot - 1}$

Step 1.4.1.1.5.2

Factor $4$ out of $- 4 \cdot - 1$ .

$m = \frac{4 (- 1 (0 + 2))}{4 (0) + 4 (1)}$

Step 1.4.1.1.5.3

Factor $4$ out of $4 (0) + 4 (- - 1)$ .

$m = \frac{4 (- 1 (0 + 2))}{4 (0 + 1)}$

Step 1.4.1.1.5.4

Cancel the common factor.

$m = \frac{4 (- 1 (0 + 2))}{4 (0 + 1)}$

Step 1.4.1.1.5.5

Rewrite the expression.

$m = \frac{- 1 (0 + 2)}{0 + 1}$

Step 1.4.1.2

Add $0$ and $2$ .

$m = \frac{- 1 \cdot 2}{0 + 1}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{- 1 \cdot 2}{0 + 1}$

Step 1.4.2.2

Add $0$ and $1$ .

$m = \frac{- 1 \cdot 2}{1}$

Step 1.4.3

Simplify the expression.

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Step 1.4.3.1

Multiply $- 1$ by $2$ .

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

Step 1.4.3.2

Divide $- 2$ by $1$ .

$m = - 2$

Step 2

Use the slope $- 2$ and a given point $(- 4, 8)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (8) = - 2 \cdot (x - (- 4))$

Step 3

Simplify the equation and keep it in point-slope form.

$y - 8 = - 2 \cdot (x + 4)$

Step 4

Solve for $y$ .

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Step 4.1

Simplify $- 2 \cdot (x + 4)$ .

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Step 4.1.1

Rewrite.

$y - 8 = 0 + 0 - 2 \cdot (x + 4)$

Step 4.1.2

Simplify by adding zeros.

$y - 8 = - 2 \cdot (x + 4)$

Step 4.1.3

Apply the distributive property.

$y - 8 = - 2 x - 2 \cdot 4$

Step 4.1.4

Multiply $- 2$ by $4$ .

$y - 8 = - 2 x - 8$

Step 4.2

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

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Step 4.2.1

Add $8$ to both sides of the equation.

$y = - 2 x - 8 + 8$

Step 4.2.2

Combine the opposite terms in $- 2 x - 8 + 8$ .

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Step 4.2.2.1

Add $- 8$ and $8$ .

$y = - 2 x + 0$

Step 4.2.2.2

Add $- 2 x$ and $0$ .

$y = - 2 x$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = - 2 x$

Point-slope form:

$y - 8 = - 2 \cdot (x + 4)$

Step 6