Find the Equation with a Point and Slope m=3/5 ; (-1,4)

$m = \frac{3}{5}$ ; $(- 1, 4)$

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.

$y = (\frac{3}{5}) x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

Rewrite the equation as $\frac{3}{5} \cdot - 1 + b = 4$ .

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

Simplify each term.

Multiply $\frac{3}{5} \cdot - 1$ .

Combine $\frac{3}{5}$ and $- 1$ .

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

Multiply $3$ by $- 1$ .

$\frac{- 3}{5} + b = 4$

Move the negative in front of the fraction.

$- \frac{3}{5} + b = 4$

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

Add $\frac{3}{5}$ to both sides of the equation.

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

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $5$ .

$b = \frac{20 + 3}{5}$

Add $20$ and $3$ .

$b = \frac{23}{5}$

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.

$y = \frac{3}{5} x + \frac{23}{5}$