Find the Equation with a Point and Slope m=2/3 , (8,1)

$m = \frac{2}{3}$ , $(8, 1)$

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$1 = (\frac{2}{3}) \cdot (8) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{2}{3} \cdot 8 + b = 1$ .

$\frac{2}{3} \cdot 8 + b = 1$

Multiply $\frac{2}{3} \cdot 8$ .

Combine $\frac{2}{3}$ and $8$ .

$\frac{2 \cdot 8}{3} + b = 1$

Multiply $2$ by $8$ .

$\frac{16}{3} + b = 1$

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

Subtract $\frac{16}{3}$ from both sides of the equation.

$b = 1 - \frac{16}{3}$

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

$b = \frac{3}{3} - \frac{16}{3}$

Combine the numerators over the common denominator.

$b = \frac{3 - 16}{3}$

Subtract $16$ from $3$ .

$b = \frac{- 13}{3}$

Move the negative in front of the fraction.

$b = - \frac{13}{3}$

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.

$y = \frac{2}{3} x - \frac{13}{3}$