Find the Point-Slope Form y-3=2(x+4)

$y - 3 = 2 (x + 4)$

Write in slope-intercept form $y = m x + b$ to identify the slope $m$ .

Solve for $y$ .

Simplify $2 (x + 4)$ .

Rewrite.

$y - 3 = 0 + 0 + 2 (x + 4)$

Simplify by adding zeros.

$y - 3 = 2 (x + 4)$

Apply the distributive property.

$y - 3 = 2 x + 2 \cdot 4$

Multiply $2$ by $4$ .

$y - 3 = 2 x + 8$

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

Add $3$ to both sides of the equation.

$y = 2 x + 8 + 3$

Add $8$ and $3$ .

$y = 2 x + 11$

Using slope-intercept form $y = m x + b$ , identify the slope $m$ .

$y = 2 x + 11$

$m = 2$

$y = 2 x + 11$

$m = 2$

Pick any $x$ -value, then substitute into the equation and simplify to find a point on the line.

Substitute $1$ for $x$ .

$y = 2 \cdot 1 + 11$

Multiply $2$ by $1$ .

$y = 2 + 11$

Add $2$ and $11$ .

$y = 13$

Since $y = 13$ when $x = 1$ , $(1, 13)$ is a point on the line.

$(1, 13)$

Plug in the values of the found point and the value of the slope into the point-slope form $y - y_{1} = m (x - x_{1})$ .

$y - 13 = 2 (x - 1)$