Find the Equation Using Slope-Intercept Form m=6/7 , (1,-3)

$m = \frac{6}{7}$ , $(1, - 3)$

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.

$y = (\frac{6}{7}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{6}{7}) \cdot (1) + b$

Substitute the value of $y$ into the equation.

$- 3 = (\frac{6}{7}) \cdot (1) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{6}{7} \cdot 1 + b = - 3$ .

$\frac{6}{7} \cdot 1 + b = - 3$

Multiply $\frac{6}{7}$ by $1$ .

$\frac{6}{7} + b = - 3$

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

Subtract $\frac{6}{7}$ from both sides of the equation.

$b = - 3 - \frac{6}{7}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$b = - 3 \cdot \frac{7}{7} - \frac{6}{7}$

Combine $- 3$ and $\frac{7}{7}$ .

$b = \frac{- 3 \cdot 7}{7} - \frac{6}{7}$

Combine the numerators over the common denominator.

$b = \frac{- 3 \cdot 7 - 6}{7}$

Simplify the numerator.

Multiply $- 3$ by $7$ .

$b = \frac{- 21 - 6}{7}$

Subtract $6$ from $- 21$ .

$b = \frac{- 27}{7}$

Move the negative in front of the fraction.

$b = - \frac{27}{7}$

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.

$y = \frac{6}{7} x - \frac{27}{7}$