Find the Equation Using Point-Slope Formula (1,-7) , slope=-1

$(1, - 7)$ , $s l o p e = - 1$

Use the slope $- 1$ and a given point $(1, - 7)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 7) = - 1 \cdot (x - (1))$

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

$y + 7 = - 1 \cdot (x - 1)$

Solve for $y$ .

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

Rewrite.

$y + 7 = 0 + 0 - 1 \cdot (x - 1)$

Simplify by adding zeros.

$y + 7 = - 1 \cdot (x - 1)$

Apply the distributive property.

$y + 7 = - 1 x - 1 \cdot - 1$

Simplify the expression.

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

$y + 7 = - x - 1 \cdot - 1$

Multiply $- 1$ by $- 1$ .

$y + 7 = - x + 1$

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

Subtract $7$ from both sides of the equation.

$y = - x + 1 - 7$

Subtract $7$ from $1$ .

$y = - x - 6$

List the equation in different forms.

Slope-intercept form:

$y = - x - 6$

Point-slope form:

$y + 7 = - 1 \cdot (x - 1)$

Find the Equation Using Point-Slope Formula (1,-7) , slope=-1

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