Find the Equation Using Slope-Intercept Form m=-5/18 , (-9,18)

$m = - \frac{5}{18}$ , $(- 9, 18)$

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.

$y = (- \frac{5}{18}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{5}{18}) \cdot (- 9) + b$

Substitute the value of $y$ into the equation.

$18 = (- \frac{5}{18}) \cdot (- 9) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{5}{18} \cdot - 9 + b = 18$ .

$- \frac{5}{18} \cdot - 9 + b = 18$

Simplify each term.

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{5}{18}$ into the numerator.

$\frac{- 5}{18} \cdot - 9 + b = 18$

Factor $9$ out of $18$ .

$\frac{- 5}{9 (2)} \cdot - 9 + b = 18$

Factor $9$ out of $- 9$ .

$\frac{- 5}{9 \cdot 2} \cdot (9 \cdot - 1) + b = 18$

Cancel the common factor.

$\frac{- 5}{9 \cdot 2} \cdot (9 \cdot - 1) + b = 18$

Rewrite the expression.

$\frac{- 5}{2} \cdot - 1 + b = 18$

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

$\frac{- 5 \cdot - 1}{2} + b = 18$

Multiply $- 5$ by $- 1$ .

$\frac{5}{2} + b = 18$

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

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

$b = 18 - \frac{5}{2}$

To write $18$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = 18 \cdot \frac{2}{2} - \frac{5}{2}$

Combine $18$ and $\frac{2}{2}$ .

$b = \frac{18 \cdot 2}{2} - \frac{5}{2}$

Combine the numerators over the common denominator.

$b = \frac{18 \cdot 2 - 5}{2}$

Simplify the numerator.

Multiply $18$ by $2$ .

$b = \frac{36 - 5}{2}$

Subtract $5$ from $36$ .

$b = \frac{31}{2}$

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.

$y = - \frac{5}{18} x + \frac{31}{2}$

Step 3

Find the Equation Using Slope-Intercept Form m=-5/18 , (-9,18)

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