Find the Point-Slope Form y+2=-4(x-1)

$y + 2 = - 4 (x - 1)$

Step 1

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

Solve for $y$ .

Simplify $- 4 (x - 1)$ .

Rewrite.

$y + 2 = 0 + 0 - 4 (x - 1)$

Simplify by adding zeros.

$y + 2 = - 4 (x - 1)$

Apply the distributive property.

$y + 2 = - 4 x - 4 \cdot - 1$

Multiply $- 4$ by $- 1$ .

$y + 2 = - 4 x + 4$

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

Subtract $2$ from both sides of the equation.

$y = - 4 x + 4 - 2$

Subtract $2$ from $4$ .

$y = - 4 x + 2$

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

$y = - 4 x + 2$

$m = - 4$

$y = - 4 x + 2$

$m = - 4$

Step 2

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

Substitute $1$ for $x$ .

$y = - 4 \cdot 1 + 2$

Multiply $- 4$ by $1$ .

$y = - 4 + 2$

Add $- 4$ and $2$ .

$y = - 2$

Since $y = - 2$ when $x = 1$ , $(1, - 2)$ is a point on the line.

$(1, - 2)$

Step 3

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

$y + 2 = - 4 (x - 1)$

Step 4