Find the Equation with a Point and Slope 1/5 , (-1,-3)

$\frac{1}{5}$ , $(- 1, - 3)$

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.

$y = (\frac{1}{5}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{1}{5}) \cdot (- 1) + b$

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

Rewrite the equation as $\frac{1}{5} \cdot - 1 + b = - 3$ .

$\frac{1}{5} \cdot - 1 + b = - 3$

Simplify each term.

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

$\frac{- 1}{5} + b = - 3$

Move the negative in front of the fraction.

$- \frac{1}{5} + b = - 3$

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

Add $\frac{1}{5}$ to both sides of the equation.

$b = - 3 + \frac{1}{5}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = - 3 \cdot \frac{5}{5} + \frac{1}{5}$

Combine $- 3$ and $\frac{5}{5}$ .

$b = \frac{- 3 \cdot 5}{5} + \frac{1}{5}$

Combine the numerators over the common denominator.

$b = \frac{- 3 \cdot 5 + 1}{5}$

Simplify the numerator.

Multiply $- 3$ by $5$ .

$b = \frac{- 15 + 1}{5}$

Add $- 15$ and $1$ .

$b = \frac{- 14}{5}$

Move the negative in front of the fraction.

$b = - \frac{14}{5}$

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.

$y = \frac{1}{5} x - \frac{14}{5}$

Step 3