Find the Equation Using Point-Slope Formula m=-5 , (2,7)

$m = - 5$ , $(2, 7)$

Step 1

Use the slope $- 5$ and a given point $(2, 7)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (7) = - 5 \cdot (x - (2))$

Step 2

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

$y - 7 = - 5 \cdot (x - 2)$

Step 3

Solve for $y$ .

Simplify $- 5 \cdot (x - 2)$ .

Rewrite.

$y - 7 = 0 + 0 - 5 \cdot (x - 2)$

Simplify by adding zeros.

$y - 7 = - 5 \cdot (x - 2)$

Apply the distributive property.

$y - 7 = - 5 x - 5 \cdot - 2$

Multiply $- 5$ by $- 2$ .

$y - 7 = - 5 x + 10$

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

Add $7$ to both sides of the equation.

$y = - 5 x + 10 + 7$

Add $10$ and $7$ .

$y = - 5 x + 17$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - 5 x + 17$

Point-slope form:

$y - 7 = - 5 \cdot (x - 2)$

Step 5

Find the Equation Using Point-Slope Formula m=-5 , (2,7)

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