Find the Equation Using Slope-Intercept Form m=-5/16 , (-8,16)

$m = - \frac{5}{16}$ , $(- 8, 16)$

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.

$y = (- \frac{5}{16}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{5}{16}) \cdot (- 8) + b$

Substitute the value of $y$ into the equation.

$16 = (- \frac{5}{16}) \cdot (- 8) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{5}{16} \cdot - 8 + b = 16$ .

$- \frac{5}{16} \cdot - 8 + b = 16$

Simplify each term.

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{5}{16}$ into the numerator.

$\frac{- 5}{16} \cdot - 8 + b = 16$

Factor $8$ out of $16$ .

$\frac{- 5}{8 (2)} \cdot - 8 + b = 16$

Factor $8$ out of $- 8$ .

$\frac{- 5}{8 \cdot 2} \cdot (8 \cdot - 1) + b = 16$

Cancel the common factor.

$\frac{- 5}{8 \cdot 2} \cdot (8 \cdot - 1) + b = 16$

Rewrite the expression.

$\frac{- 5}{2} \cdot - 1 + b = 16$

Combine $\frac{- 5}{2}$ and $- 1$ .

$\frac{- 5 \cdot - 1}{2} + b = 16$

Multiply $- 5$ by $- 1$ .

$\frac{5}{2} + b = 16$

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

Subtract $\frac{5}{2}$ from both sides of the equation.

$b = 16 - \frac{5}{2}$

To write $16$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = 16 \cdot \frac{2}{2} - \frac{5}{2}$

Combine $16$ and $\frac{2}{2}$ .

$b = \frac{16 \cdot 2}{2} - \frac{5}{2}$

Combine the numerators over the common denominator.

$b = \frac{16 \cdot 2 - 5}{2}$

Simplify the numerator.

Multiply $16$ by $2$ .

$b = \frac{32 - 5}{2}$

Subtract $5$ from $32$ .

$b = \frac{27}{2}$

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.

$y = - \frac{5}{16} x + \frac{27}{2}$

Step 3

Find the Equation Using Slope-Intercept Form m=-5/16 , (-8,16)

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