Find the Equation Using Slope-Intercept Form (-6,-8) , m=3/4

$(- 6, - 8)$ , $m = \frac{3}{4}$

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.

$y = (\frac{3}{4}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{3}{4}) \cdot (- 6) + b$

Substitute the value of $y$ into the equation.

$- 8 = (\frac{3}{4}) \cdot (- 6) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{3}{4} \cdot - 6 + b = - 8$ .

$\frac{3}{4} \cdot - 6 + b = - 8$

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3}{2 (2)} \cdot - 6 + b = - 8$

Factor $2$ out of $- 6$ .

$\frac{3}{2 \cdot 2} \cdot (2 \cdot - 3) + b = - 8$

Cancel the common factor.

$\frac{3}{2 \cdot 2} \cdot (2 \cdot - 3) + b = - 8$

Rewrite the expression.

$\frac{3}{2} \cdot - 3 + b = - 8$

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

$\frac{3 \cdot - 3}{2} + b = - 8$

Multiply $3$ by $- 3$ .

$\frac{- 9}{2} + b = - 8$

Move the negative in front of the fraction.

$- \frac{9}{2} + b = - 8$

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

Add $\frac{9}{2}$ to both sides of the equation.

$b = - 8 + \frac{9}{2}$

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = - 8 \cdot \frac{2}{2} + \frac{9}{2}$

Combine $- 8$ and $\frac{2}{2}$ .

$b = \frac{- 8 \cdot 2}{2} + \frac{9}{2}$

Combine the numerators over the common denominator.

$b = \frac{- 8 \cdot 2 + 9}{2}$

Simplify the numerator.

Multiply $- 8$ by $2$ .

$b = \frac{- 16 + 9}{2}$

Add $- 16$ and $9$ .

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

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.

$y = \frac{3}{4} x - \frac{7}{2}$

Step 3

Find the Equation Using Slope-Intercept Form (-6,-8) , m=3/4

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