Find the Equation Using Point-Slope Formula through: (2,-4) , slope=-1

through: $(2, - 4)$ , $s l o p e = - 1$

Step 1

Use the slope $- 1$ and a given point $(2, - 4)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 4) = - 1 \cdot (x - (2))$

Step 2

Simplify the equation and keep it in point-slope form.

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

Step 3

Solve for $y$ .

Simplify $- 1 \cdot (x - 2)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Simplify the expression.

Rewrite $- 1 x$ as $- x$ .

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

Multiply $- 1$ by $- 2$ .

$y + 4 = - x + 2$

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

Subtract $4$ from both sides of the equation.

$y = - x + 2 - 4$

Subtract $4$ from $2$ .

$y = - x - 2$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - x - 2$

Point-slope form:

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

Step 5

Find the Equation Using Point-Slope Formula through: (2,-4) , slope=-1

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