Find the Equation Using Slope-Intercept Form (-4,1) ; m=-2/3

$(- 4, 1)$ ; $m = - \frac{2}{3}$

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.

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

Substitute the value of $x$ into the equation.

$y = (- \frac{2}{3}) \cdot (- 4) + b$

Substitute the value of $y$ into the equation.

$1 = (- \frac{2}{3}) \cdot (- 4) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{2}{3} \cdot - 4 + b = 1$ .

$- \frac{2}{3} \cdot - 4 + b = 1$

Multiply $- \frac{2}{3} \cdot - 4$ .

Multiply $- 4$ by $- 1$ .

$4 (\frac{2}{3}) + b = 1$

Combine $4$ and $\frac{2}{3}$ .

$\frac{4 \cdot 2}{3} + b = 1$

Multiply $4$ by $2$ .

$\frac{8}{3} + b = 1$

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

Subtract $\frac{8}{3}$ from both sides of the equation.

$b = 1 - \frac{8}{3}$

Write $1$ as a fraction with a common denominator.

$b = \frac{3}{3} - \frac{8}{3}$

Combine the numerators over the common denominator.

$b = \frac{3 - 8}{3}$

Subtract $8$ from $3$ .

$b = \frac{- 5}{3}$

Move the negative in front of the fraction.

$b = - \frac{5}{3}$

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.

$y = - \frac{2}{3} x - \frac{5}{3}$

Step 3