Find the Equation with a Point and Slope What is the equation of the line that passes through the point (8,8) and has a slope of 2 ?

What is the equation of the line that passes through the point $(8, 8)$ and has a slope of $2$ ?

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.

$y = (2) \cdot (8) + b$

Substitute the value of $y$ into the equation.

$8 = (2) \cdot (8) + b$

Find the value of $b$ .

Rewrite the equation as $(2) \cdot (8) + b = 8$ .

$(2) \cdot (8) + b = 8$

Multiply $2$ by $8$ .

$16 + b = 8$

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

Subtract $16$ from both sides of the equation.

$b = 8 - 16$

Subtract $16$ from $8$ .

$b = - 8$

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.

$y = 2 x - 8$

Step 3