Algebra Examples

$m = - \frac{1}{8}$ , $(- 6, 0)$

Step 1

Use the slope $- \frac{1}{8}$ and a given point $(- 6, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{1}{8} \cdot (x - (- 6))$

Step 2

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

$y + 0 = - \frac{1}{8} \cdot (x + 6)$

Step 3

Solve for $y$ .

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Step 3.1

Add $y$ and $0$ .

$y = - \frac{1}{8} \cdot (x + 6)$

Step 3.2

Simplify $- \frac{1}{8} \cdot (x + 6)$ .

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Step 3.2.1

Apply the distributive property.

$y = - \frac{1}{8} x - \frac{1}{8} \cdot 6$

Step 3.2.2

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

$y = - \frac{x}{8} - \frac{1}{8} \cdot 6$

Step 3.2.3

Cancel the common factor of $2$ .

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Step 3.2.3.1

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

$y = - \frac{x}{8} + \frac{- 1}{8} \cdot 6$

Step 3.2.3.2

Factor $2$ out of $8$ .

$y = - \frac{x}{8} + \frac{- 1}{2 (4)} \cdot 6$

Step 3.2.3.3

Factor $2$ out of $6$ .

$y = - \frac{x}{8} + \frac{- 1}{2 \cdot 4} \cdot (2 \cdot 3)$

Step 3.2.3.4

Cancel the common factor.

$y = - \frac{x}{8} + \frac{- 1}{2 \cdot 4} \cdot (2 \cdot 3)$

Step 3.2.3.5

Rewrite the expression.

$y = - \frac{x}{8} + \frac{- 1}{4} \cdot 3$

Step 3.2.4

Combine $\frac{- 1}{4}$ and $3$ .

$y = - \frac{x}{8} + \frac{- 1 \cdot 3}{4}$

Step 3.2.5

Simplify the expression.

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Step 3.2.5.1

Multiply $- 1$ by $3$ .

$y = - \frac{x}{8} + \frac{- 3}{4}$

Step 3.2.5.2

Move the negative in front of the fraction.

$y = - \frac{x}{8} - \frac{3}{4}$

Step 3.3

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

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Step 3.3.1

Reorder terms.

$y = - (\frac{1}{8} x) - \frac{3}{4}$

Step 3.3.2

Remove parentheses.

$y = - \frac{1}{8} x - \frac{3}{4}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - \frac{1}{8} x - \frac{3}{4}$

Point-slope form:

$y + 0 = - \frac{1}{8} \cdot (x + 6)$

Step 5