Find the Equation Using Slope-Intercept Form (-4,7) ; m=-3/4

$(- 4, 7)$ ; $m = - \frac{3}{4}$

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$7 = (- \frac{3}{4}) \cdot (- 4) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{3}{4} \cdot - 4 + b = 7$ .

$- \frac{3}{4} \cdot - 4 + b = 7$

Simplify each term.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} \cdot - 4 + b = 7$

Factor $4$ out of $- 4$ .

$\frac{- 3}{4} \cdot (4 (- 1)) + b = 7$

Cancel the common factor.

$\frac{- 3}{4} \cdot (4 \cdot - 1) + b = 7$

Rewrite the expression.

$- 3 \cdot - 1 + b = 7$

Multiply $- 3$ by $- 1$ .

$3 + b = 7$

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

Subtract $3$ from both sides of the equation.

$b = 7 - 3$

Subtract $3$ from $7$ .

$b = 4$

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.

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

Step 3