Find the Equation Using Slope-Intercept Form m=1/2 , (-7,8)

$m = \frac{1}{2}$ , $(- 7, 8)$

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.

$y = (\frac{1}{2}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{1}{2}) \cdot (- 7) + b$

Substitute the value of $y$ into the equation.

$8 = (\frac{1}{2}) \cdot (- 7) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{1}{2} \cdot - 7 + b = 8$ .

$\frac{1}{2} \cdot - 7 + b = 8$

Simplify each term.

Combine $\frac{1}{2}$ and $- 7$ .

$\frac{- 7}{2} + b = 8$

Move the negative in front of the fraction.

$- \frac{7}{2} + b = 8$

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

Add $\frac{7}{2}$ to both sides of the equation.

$b = 8 + \frac{7}{2}$

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = 8 \cdot \frac{2}{2} + \frac{7}{2}$

Combine $8$ and $\frac{2}{2}$ .

$b = \frac{8 \cdot 2}{2} + \frac{7}{2}$

Combine the numerators over the common denominator.

$b = \frac{8 \cdot 2 + 7}{2}$

Simplify the numerator.

Multiply $8$ by $2$ .

$b = \frac{16 + 7}{2}$

Add $16$ and $7$ .

$b = \frac{23}{2}$

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.

$y = \frac{1}{2} x + \frac{23}{2}$

Step 3