Algebra Examples

$m = - \frac{1}{10}$ , $(- 9, 0)$

Step 1

Use the slope $- \frac{1}{10}$ and a given point $(- 9, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{1}{10} \cdot (x - (- 9))$

Step 2

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

$y + 0 = - \frac{1}{10} \cdot (x + 9)$

Step 3

Solve for $y$ .

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Step 3.1

Add $y$ and $0$ .

$y = - \frac{1}{10} \cdot (x + 9)$

Step 3.2

Simplify $- \frac{1}{10} \cdot (x + 9)$ .

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Step 3.2.1

Apply the distributive property.

$y = - \frac{1}{10} x - \frac{1}{10} \cdot 9$

Step 3.2.2

Combine $x$ and $\frac{1}{10}$ .

$y = - \frac{x}{10} - \frac{1}{10} \cdot 9$

Step 3.2.3

Multiply $- \frac{1}{10} \cdot 9$ .

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Step 3.2.3.1

Multiply $9$ by $- 1$ .

$y = - \frac{x}{10} - 9 (\frac{1}{10})$

Step 3.2.3.2

Combine $- 9$ and $\frac{1}{10}$ .

$y = - \frac{x}{10} + \frac{- 9}{10}$

Step 3.2.4

Move the negative in front of the fraction.

$y = - \frac{x}{10} - \frac{9}{10}$

Step 3.3

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

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Step 3.3.1

Reorder terms.

$y = - (\frac{1}{10} x) - \frac{9}{10}$

Step 3.3.2

Remove parentheses.

$y = - \frac{1}{10} x - \frac{9}{10}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - \frac{1}{10} x - \frac{9}{10}$

Point-slope form:

$y + 0 = - \frac{1}{10} \cdot (x + 9)$

Step 5