Find the Equation Using Slope-Intercept Form m=-7/12 , (-6,12)

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

Step 1

Find the value of $b$ using the formula for the equation of a line.

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

Rewrite the equation as $- \frac{7}{12} \cdot - 6 + b = 12$ .

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

Simplify each term.

Cancel the common factor of $6$ .

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

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

Factor $6$ out of $12$ .

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

Factor $6$ out of $- 6$ .

$\frac{- 7}{6 \cdot 2} \cdot (6 \cdot - 1) + b = 12$

Cancel the common factor.

$\frac{- 7}{6 \cdot 2} \cdot (6 \cdot - 1) + b = 12$

Rewrite the expression.

$\frac{- 7}{2} \cdot - 1 + b = 12$

Combine $\frac{- 7}{2}$ and $- 1$ .

$\frac{- 7 \cdot - 1}{2} + b = 12$

Multiply $- 7$ by $- 1$ .

$\frac{7}{2} + b = 12$

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

Subtract $\frac{7}{2}$ from both sides of the equation.

$b = 12 - \frac{7}{2}$

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

$b = 12 \cdot \frac{2}{2} - \frac{7}{2}$

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

$b = \frac{12 \cdot 2}{2} - \frac{7}{2}$

Combine the numerators over the common denominator.

$b = \frac{12 \cdot 2 - 7}{2}$

Simplify the numerator.

Multiply $12$ by $2$ .

$b = \frac{24 - 7}{2}$

Subtract $7$ from $24$ .

$b = \frac{17}{2}$

Step 2

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

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

Step 3

Find the Equation Using Slope-Intercept Form m=-7/12 , (-6,12)

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