Find the Equation with a Point and Slope What is the equation of the line that passes through the point (-5,0) and has a slope of 3/5 ?

What is the equation of the line that passes through the point $(- 5, 0)$ and has a slope of $\frac{3}{5}$ ?

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.

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

Substitute the value of $y$ into the equation.

$0 = (\frac{3}{5}) \cdot (- 5) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{3}{5} \cdot - 5 + b = 0$ .

$\frac{3}{5} \cdot - 5 + b = 0$

Simplify each term.

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$\frac{3}{5} \cdot (5 (- 1)) + b = 0$

Cancel the common factor.

$\frac{3}{5} \cdot (5 \cdot - 1) + b = 0$

Rewrite the expression.

$3 \cdot - 1 + b = 0$

Multiply $3$ by $- 1$ .

$- 3 + b = 0$

Add $3$ to both sides of the equation.

$b = 3$

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.

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