Find the Equation with a Point and Slope What is the equation of the line that passes through the point (-3,7) and has a slope of -3 ?

What is the equation of the line that passes through the point $(- 3, 7)$ and has a slope of $- 3$ ?

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$7 = (- 3) \cdot (- 3) + b$

Find the value of $b$ .

Rewrite the equation as $(- 3) \cdot (- 3) + b = 7$ .

$(- 3) \cdot (- 3) + b = 7$

Multiply $- 3$ by $- 3$ .

$9 + b = 7$

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

Subtract $9$ from both sides of the equation.

$b = 7 - 9$

Subtract $9$ from $7$ .

$b = - 2$

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.

$y = - 3 x - 2$

Step 3