Algebra Examples

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

Step 1

Use the slope $- \frac{1}{8}$ and a given point $(- 4, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

Step 2

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

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

Step 3

Solve for $y$ .

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Step 3.1

Add $y$ and $0$ .

$y = - \frac{1}{8} \cdot (x + 4)$

Step 3.2

Simplify $- \frac{1}{8} \cdot (x + 4)$ .

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Step 3.2.1

Apply the distributive property.

$y = - \frac{1}{8} x - \frac{1}{8} \cdot 4$

Step 3.2.2

Combine $x$ and $\frac{1}{8}$ .

$y = - \frac{x}{8} - \frac{1}{8} \cdot 4$

Step 3.2.3

Cancel the common factor of $4$ .

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Step 3.2.3.1

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$y = - \frac{x}{8} + \frac{- 1}{8} \cdot 4$

Step 3.2.3.2

Factor $4$ out of $8$ .

$y = - \frac{x}{8} + \frac{- 1}{4 (2)} \cdot 4$

Step 3.2.3.3

Cancel the common factor.

$y = - \frac{x}{8} + \frac{- 1}{4 \cdot 2} \cdot 4$

Step 3.2.3.4

Rewrite the expression.

$y = - \frac{x}{8} + \frac{- 1}{2}$

Step 3.2.4

Move the negative in front of the fraction.

$y = - \frac{x}{8} - \frac{1}{2}$

Step 3.3

Write in $y = m x + b$ form.

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Step 3.3.1

Reorder terms.

$y = - (\frac{1}{8} x) - \frac{1}{2}$

Step 3.3.2

Remove parentheses.

$y = - \frac{1}{8} x - \frac{1}{2}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - \frac{1}{8} x - \frac{1}{2}$

Point-slope form:

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

Step 5