Find the Equation with a Point and Slope (3,-11) , -2

$(3, - 11)$ , $- 2$

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.

$- 11 = (- 2) \cdot (3) + b$

Find the value of $b$ .

Rewrite the equation as $(- 2) \cdot (3) + b = - 11$ .

$(- 2) \cdot (3) + b = - 11$

Multiply $- 2$ by $3$ .

$- 6 + b = - 11$

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

Add $6$ to both sides of the equation.

$b = - 11 + 6$

Add $- 11$ and $6$ .

$b = - 5$

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.

$y = - 2 x - 5$

Step 3