Find the Equation with a Point and Slope What is the equation of the line that passes through the point (-4,-3) and has a slope of 3/4 ?

What is the equation of the line that passes through the point $(- 4, - 3)$ and has a slope of $\frac{3}{4}$ ?

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.

$y = (\frac{3}{4}) x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

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

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

Simplify each term.

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$3 \cdot - 1 + b = - 3$

Multiply $3$ by $- 1$ .

$- 3 + b = - 3$

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

Add $3$ to both sides of the equation.

$b = - 3 + 3$

Add $- 3$ and $3$ .

$b = 0$

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.

$y = \frac{3}{4} x$

Step 3