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

What is the equation of the line that passes through the point $(2, - 2)$ 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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

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

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$- 1 + b = - 2$

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

Add $1$ to both sides of the equation.

$b = - 2 + 1$

Add $- 2$ and $1$ .

$b = - 1$

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.

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