Find the Equation Using Slope-Intercept Form (-9,-11) , m=5/6

$(- 9, - 11)$ , $m = \frac{5}{6}$

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.

$y = (\frac{5}{6}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{5}{6}) \cdot (- 9) + b$

Substitute the value of $y$ into the equation.

$- 11 = (\frac{5}{6}) \cdot (- 9) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{5}{6} \cdot - 9 + b = - 11$ .

$\frac{5}{6} \cdot - 9 + b = - 11$

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{5}{3 (2)} \cdot - 9 + b = - 11$

Factor $3$ out of $- 9$ .

$\frac{5}{3 \cdot 2} \cdot (3 \cdot - 3) + b = - 11$

Cancel the common factor.

$\frac{5}{3 \cdot 2} \cdot (3 \cdot - 3) + b = - 11$

Rewrite the expression.

$\frac{5}{2} \cdot - 3 + b = - 11$

Combine $\frac{5}{2}$ and $- 3$ .

$\frac{5 \cdot - 3}{2} + b = - 11$

Multiply $5$ by $- 3$ .

$\frac{- 15}{2} + b = - 11$

Move the negative in front of the fraction.

$- \frac{15}{2} + b = - 11$

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

Add $\frac{15}{2}$ to both sides of the equation.

$b = - 11 + \frac{15}{2}$

To write $- 11$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = - 11 \cdot \frac{2}{2} + \frac{15}{2}$

Combine $- 11$ and $\frac{2}{2}$ .

$b = \frac{- 11 \cdot 2}{2} + \frac{15}{2}$

Combine the numerators over the common denominator.

$b = \frac{- 11 \cdot 2 + 15}{2}$

Simplify the numerator.

Multiply $- 11$ by $2$ .

$b = \frac{- 22 + 15}{2}$

Add $- 22$ and $15$ .

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

Move the negative in front of the fraction.

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

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.

$y = \frac{5}{6} x - \frac{7}{2}$

Step 3

Find the Equation Using Slope-Intercept Form (-9,-11) , m=5/6

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