Find the Equation Using Point-Slope Formula m=5/6 , (30,12)

$m = \frac{5}{6}$ , $(30, 12)$

Step 1

Use the slope $\frac{5}{6}$ and a given point $(30, 12)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (12) = \frac{5}{6} \cdot (x - (30))$

Step 2

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

$y - 12 = \frac{5}{6} \cdot (x - 30)$

Step 3

Solve for $y$ .

Simplify $\frac{5}{6} \cdot (x - 30)$ .

Rewrite.

$y - 12 = 0 + 0 + \frac{5}{6} \cdot (x - 30)$

Simplify by adding zeros.

$y - 12 = \frac{5}{6} \cdot (x - 30)$

Apply the distributive property.

$y - 12 = \frac{5}{6} x + \frac{5}{6} \cdot - 30$

Combine $\frac{5}{6}$ and $x$ .

$y - 12 = \frac{5 x}{6} + \frac{5}{6} \cdot - 30$

Cancel the common factor of $6$ .

Factor $6$ out of $- 30$ .

$y - 12 = \frac{5 x}{6} + \frac{5}{6} \cdot (6 (- 5))$

Cancel the common factor.

$y - 12 = \frac{5 x}{6} + \frac{5}{6} \cdot (6 \cdot - 5)$

Rewrite the expression.

$y - 12 = \frac{5 x}{6} + 5 \cdot - 5$

Multiply $5$ by $- 5$ .

$y - 12 = \frac{5 x}{6} - 25$

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

Add $12$ to both sides of the equation.

$y = \frac{5 x}{6} - 25 + 12$

Add $- 25$ and $12$ .

$y = \frac{5 x}{6} - 13$

Reorder terms.

$y = \frac{5}{6} x - 13$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = \frac{5}{6} x - 13$

Point-slope form:

$y - 12 = \frac{5}{6} \cdot (x - 30)$

Step 5

Find the Equation Using Point-Slope Formula m=5/6 , (30,12)

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