Find the Equation with a Point and Slope What is the equation of the line that passes through the point (2,-4) and has a slope of 2 ?

What is the equation of the line that passes through the point $(2, - 4)$ 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.

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

Substitute the value of $y$ into the equation.

$- 4 = (2) \cdot (2) + b$

Find the value of $b$ .

Rewrite the equation as $(2) \cdot (2) + b = - 4$ .

$(2) \cdot (2) + b = - 4$

Multiply $2$ by $2$ .

$4 + b = - 4$

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

Subtract $4$ from both sides of the equation.

$b = - 4 - 4$

Subtract $4$ from $- 4$ .

$b = - 8$

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.

$y = 2 x - 8$