Find the Equation with a Point and Slope What is the equation of the line that passes through the point (-2,5) and has a slope of -4 ?

What is the equation of the line that passes through the point $(- 2, 5)$ and has a slope of $- 4$ ?

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.

$y = (- 4) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- 4) \cdot (- 2) + b$

Substitute the value of $y$ into the equation.

$5 = (- 4) \cdot (- 2) + b$

Find the value of $b$ .

Rewrite the equation as $(- 4) \cdot (- 2) + b = 5$ .

$(- 4) \cdot (- 2) + b = 5$

Multiply $- 4$ by $- 2$ .

$8 + b = 5$

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

Subtract $8$ from both sides of the equation.

$b = 5 - 8$

Subtract $8$ from $5$ .

$b = - 3$

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.

$y = - 4 x - 3$

Step 3