Find the Equation with a Point and Slope (8,-3) ; m=-1/4

$(8, - 3)$ ; $m = - \frac{1}{4}$

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.

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

Substitute the value of $x$ into the equation.

$y = (- \frac{1}{4}) \cdot (8) + b$

Substitute the value of $y$ into the equation.

$- 3 = (- \frac{1}{4}) \cdot (8) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{1}{4} \cdot 8 + b = - 3$ .

$- \frac{1}{4} \cdot 8 + b = - 3$

Simplify each term.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{- 1}{4} \cdot 8 + b = - 3$

Factor $4$ out of $8$ .

$\frac{- 1}{4} \cdot (4 (2)) + b = - 3$

Cancel the common factor.

$\frac{- 1}{4} \cdot (4 \cdot 2) + b = - 3$

Rewrite the expression.

$- 1 \cdot 2 + b = - 3$

Multiply $- 1$ by $2$ .

$- 2 + b = - 3$

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

Add $2$ to both sides of the equation.

$b = - 3 + 2$

Add $- 3$ and $2$ .

$b = - 1$

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.

$y = - \frac{1}{4} x - 1$

Step 3