Find the Equation Using Point-Slope Formula m=-7/12 , (-6,12)

$m = - \frac{7}{12}$ , $(- 6, 12)$

Step 1

Use the slope $- \frac{7}{12}$ and a given point $(- 6, 12)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (12) = - \frac{7}{12} \cdot (x - (- 6))$

Step 2

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

$y - 12 = - \frac{7}{12} \cdot (x + 6)$

Step 3

Solve for $y$ .

Simplify $- \frac{7}{12} \cdot (x + 6)$ .

Rewrite.

$y - 12 = 0 + 0 - \frac{7}{12} \cdot (x + 6)$

Simplify terms.

Apply the distributive property.

$y - 12 = - \frac{7}{12} x - \frac{7}{12} \cdot 6$

Combine $x$ and $\frac{7}{12}$ .

$y - 12 = - \frac{x \cdot 7}{12} - \frac{7}{12} \cdot 6$

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{7}{12}$ into the numerator.

$y - 12 = - \frac{x \cdot 7}{12} + \frac{- 7}{12} \cdot 6$

Factor $6$ out of $12$ .

$y - 12 = - \frac{x \cdot 7}{12} + \frac{- 7}{6 (2)} \cdot 6$

Cancel the common factor.

$y - 12 = - \frac{x \cdot 7}{12} + \frac{- 7}{6 \cdot 2} \cdot 6$

Rewrite the expression.

$y - 12 = - \frac{x \cdot 7}{12} + \frac{- 7}{2}$

Simplify each term.

Move $7$ to the left of $x$ .

$y - 12 = - \frac{7 \cdot x}{12} + \frac{- 7}{2}$

Move the negative in front of the fraction.

$y - 12 = - \frac{7 x}{12} - \frac{7}{2}$

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

Add $12$ to both sides of the equation.

$y = - \frac{7 x}{12} - \frac{7}{2} + 12$

To write $12$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{7 x}{12} - \frac{7}{2} + 12 \cdot \frac{2}{2}$

Combine $12$ and $\frac{2}{2}$ .

$y = - \frac{7 x}{12} - \frac{7}{2} + \frac{12 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = - \frac{7 x}{12} + \frac{- 7 + 12 \cdot 2}{2}$

Simplify the numerator.

Multiply $12$ by $2$ .

$y = - \frac{7 x}{12} + \frac{- 7 + 24}{2}$

Add $- 7$ and $24$ .

$y = - \frac{7 x}{12} + \frac{17}{2}$

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

Reorder terms.

$y = - (\frac{7}{12} x) + \frac{17}{2}$

Remove parentheses.

$y = - \frac{7}{12} x + \frac{17}{2}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - \frac{7}{12} x + \frac{17}{2}$

Point-slope form:

$y - 12 = - \frac{7}{12} \cdot (x + 6)$

Step 5

Find the Equation Using Point-Slope Formula m=-7/12 , (-6,12)

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