Find the Equation Using Slope-Intercept Form m=-7 , (1/2,5)

$m = - 7$ , $(\frac{1}{2}, 5)$

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.

$y = (- 7) \cdot x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$5 = (- 7) \cdot (\frac{1}{2}) + b$

Find the value of $b$ .

Rewrite the equation as $- 7 \cdot \frac{1}{2} + b = 5$ .

$- 7 \cdot \frac{1}{2} + b = 5$

Simplify each term.

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

$\frac{- 7}{2} + b = 5$

Move the negative in front of the fraction.

$- \frac{7}{2} + b = 5$

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

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

$b = 5 + \frac{7}{2}$

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = 5 \cdot \frac{2}{2} + \frac{7}{2}$

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

$b = \frac{5 \cdot 2}{2} + \frac{7}{2}$

Combine the numerators over the common denominator.

$b = \frac{5 \cdot 2 + 7}{2}$

Simplify the numerator.

Multiply $5$ by $2$ .

$b = \frac{10 + 7}{2}$

Add $10$ and $7$ .

$b = \frac{17}{2}$

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.

$y = - 7 x + \frac{17}{2}$

Step 3