Find the Equation with a Point and Slope (-3,-6) , 4/15

$(- 3, - 6)$ , $\frac{4}{15}$

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.

$y = (\frac{4}{15}) \cdot (- 3) + b$

Substitute the value of $y$ into the equation.

$- 6 = (\frac{4}{15}) \cdot (- 3) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{4}{15} \cdot - 3 + b = - 6$ .

$\frac{4}{15} \cdot - 3 + b = - 6$

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$\frac{4}{3 (5)} \cdot - 3 + b = - 6$

Factor $3$ out of $- 3$ .

$\frac{4}{3 \cdot 5} \cdot (3 \cdot - 1) + b = - 6$

Cancel the common factor.

$\frac{4}{3 \cdot 5} \cdot (3 \cdot - 1) + b = - 6$

Rewrite the expression.

$\frac{4}{5} \cdot - 1 + b = - 6$

Combine $\frac{4}{5}$ and $- 1$ .

$\frac{4 \cdot - 1}{5} + b = - 6$

Multiply $4$ by $- 1$ .

$\frac{- 4}{5} + b = - 6$

Move the negative in front of the fraction.

$- \frac{4}{5} + b = - 6$

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

Add $\frac{4}{5}$ to both sides of the equation.

$b = - 6 + \frac{4}{5}$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = - 6 \cdot \frac{5}{5} + \frac{4}{5}$

Combine $- 6$ and $\frac{5}{5}$ .

$b = \frac{- 6 \cdot 5}{5} + \frac{4}{5}$

Combine the numerators over the common denominator.

$b = \frac{- 6 \cdot 5 + 4}{5}$

Simplify the numerator.

Multiply $- 6$ by $5$ .

$b = \frac{- 30 + 4}{5}$

Add $- 30$ and $4$ .

$b = \frac{- 26}{5}$

Move the negative in front of the fraction.

$b = - \frac{26}{5}$

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.

$y = \frac{4}{15} x - \frac{26}{5}$

Step 3

Find the Equation with a Point and Slope (-3,-6) , 4/15

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