Find the Equation with a Point and Slope 6 , (-6,6)

$6$ , $(- 6, 6)$

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.

$y = (6) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (6) \cdot (- 6) + b$

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

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

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

Multiply $6$ by $- 6$ .

$- 36 + b = 6$

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

Add $36$ to both sides of the equation.

$b = 6 + 36$

Add $6$ and $36$ .

$b = 42$

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.

$y = 6 x + 42$

Step 3