Find the Equation with a Point and Slope What is the equation of the line that passes through the point (3,-2) and has a slope of -2 ?

What is the equation of the line that passes through the point $(3, - 2)$ and has a slope of $- 2$ ?

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.

$y = (- 2) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- 2) \cdot (3) + b$

Substitute the value of $y$ into the equation.

$- 2 = (- 2) \cdot (3) + b$

Find the value of $b$ .

Rewrite the equation as $(- 2) \cdot (3) + b = - 2$ .

$(- 2) \cdot (3) + b = - 2$

Multiply $- 2$ by $3$ .

$- 6 + b = - 2$

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

Add $6$ to both sides of the equation.

$b = - 2 + 6$

Add $- 2$ and $6$ .

$b = 4$

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.

$y = - 2 x + 4$

Step 3