Find the Equation with a Point and Slope What is the equation of the line that passes through the point (7,-6) and has a slope of -2 ?

What is the equation of the line that passes through the point $(7, - 6)$ 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.

$y = (- 2) \cdot (7) + b$

Substitute the value of $y$ into the equation.

$- 6 = (- 2) \cdot (7) + b$

Find the value of $b$ .

Rewrite the equation as $(- 2) \cdot (7) + b = - 6$ .

$(- 2) \cdot (7) + b = - 6$

Multiply $- 2$ by $7$ .

$- 14 + b = - 6$

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

Add $14$ to both sides of the equation.

$b = - 6 + 14$

Add $- 6$ and $14$ .

$b = 8$

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.

$y = - 2 x + 8$