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

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

Step 1

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

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

Step 2

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

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

Step 3

Solve for $y$ .

Simplify $5 \cdot (x - 7)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $5$ by $- 7$ .

$y - 7 = 5 x - 35$

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

Add $7$ to both sides of the equation.

$y = 5 x - 35 + 7$

Add $- 35$ and $7$ .

$y = 5 x - 28$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = 5 x - 28$

Point-slope form:

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

Step 5

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

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