Find the Equation with a Point and Slope What is the equation of the line that passes through the point (8,-4) and has a slope of 1/2 ?

What is the equation of the line that passes through the point $(8, - 4)$ and has a slope of $\frac{1}{2}$ ?

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.

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

Substitute the value of $y$ into the equation.

$- 4 = (\frac{1}{2}) \cdot (8) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{1}{2} \cdot 8 + b = - 4$ .

$\frac{1}{2} \cdot 8 + b = - 4$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$4 + b = - 4$

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

Subtract $4$ from both sides of the equation.

$b = - 4 - 4$

Subtract $4$ from $- 4$ .

$b = - 8$

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.

$y = \frac{1}{2} x - 8$