Find the Equation with a Point and Slope What is the equation of the line that passes through the point (-3,5) and has a slope of -2 ?

What is the equation of the line that passes through the point $(- 3, 5)$ and has a slope of $- 2$ ?

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.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$5 = (- 2) \cdot (- 3) + b$

Find the value of $b$ .

Rewrite the equation as $(- 2) \cdot (- 3) + b = 5$ .

$(- 2) \cdot (- 3) + b = 5$

Multiply $- 2$ by $- 3$ .

$6 + b = 5$

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

Subtract $6$ from both sides of the equation.

$b = 5 - 6$

Subtract $6$ from $5$ .

$b = - 1$

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.

$y = - 2 x - 1$