Find the Equation Using Slope-Intercept Form m=2/15 ; passes through (5,7)

$m = \frac{2}{15}$ ; passes through $(5, 7)$

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.

$y = (\frac{2}{15}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{2}{15}) \cdot (5) + b$

Substitute the value of $y$ into the equation.

$7 = (\frac{2}{15}) \cdot (5) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{2}{15} \cdot 5 + b = 7$ .

$\frac{2}{15} \cdot 5 + b = 7$

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$\frac{2}{5 (3)} \cdot 5 + b = 7$

Cancel the common factor.

$\frac{2}{5 \cdot 3} \cdot 5 + b = 7$

Rewrite the expression.

$\frac{2}{3} + b = 7$

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

Subtract $\frac{2}{3}$ from both sides of the equation.

$b = 7 - \frac{2}{3}$

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

$b = 7 \cdot \frac{3}{3} - \frac{2}{3}$

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

$b = \frac{7 \cdot 3}{3} - \frac{2}{3}$

Combine the numerators over the common denominator.

$b = \frac{7 \cdot 3 - 2}{3}$

Simplify the numerator.

Multiply $7$ by $3$ .

$b = \frac{21 - 2}{3}$

Subtract $2$ from $21$ .

$b = \frac{19}{3}$

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.

$y = \frac{2}{15} x + \frac{19}{3}$

Step 3