Find the Equation Using Slope-Intercept Form m=4/15 ; passes through (5,9)

$m = \frac{4}{15}$ ; passes through $(5, 9)$

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.

$y = (\frac{4}{15}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{4}{15}) \cdot (5) + b$

Substitute the value of $y$ into the equation.

$9 = (\frac{4}{15}) \cdot (5) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{4}{15} \cdot 5 + b = 9$ .

$\frac{4}{15} \cdot 5 + b = 9$

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$\frac{4}{5 (3)} \cdot 5 + b = 9$

Cancel the common factor.

$\frac{4}{5 \cdot 3} \cdot 5 + b = 9$

Rewrite the expression.

$\frac{4}{3} + b = 9$

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

Subtract $\frac{4}{3}$ from both sides of the equation.

$b = 9 - \frac{4}{3}$

To write $9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = 9 \cdot \frac{3}{3} - \frac{4}{3}$

Combine $9$ and $\frac{3}{3}$ .

$b = \frac{9 \cdot 3}{3} - \frac{4}{3}$

Combine the numerators over the common denominator.

$b = \frac{9 \cdot 3 - 4}{3}$

Simplify the numerator.

Multiply $9$ by $3$ .

$b = \frac{27 - 4}{3}$

Subtract $4$ from $27$ .

$b = \frac{23}{3}$

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.

$y = \frac{4}{15} x + \frac{23}{3}$

Step 3