Precalculus Examples

$m = \frac{1}{3}$ , $(2, 3)$

Step 1

Use the slope $\frac{1}{3}$ and a given point $(2, 3)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (3) = \frac{1}{3} \cdot (x - (2))$

Step 2

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

$y - 3 = \frac{1}{3} \cdot (x - 2)$

Step 3

Solve for $y$ .

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Step 3.1

Simplify $\frac{1}{3} \cdot (x - 2)$ .

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Step 3.1.1

Rewrite.

$y - 3 = 0 + 0 + \frac{1}{3} \cdot (x - 2)$

Step 3.1.2

Simplify by adding zeros.

$y - 3 = \frac{1}{3} \cdot (x - 2)$

Step 3.1.3

Apply the distributive property.

$y - 3 = \frac{1}{3} x + \frac{1}{3} \cdot - 2$

Step 3.1.4

Combine $\frac{1}{3}$ and $x$ .

$y - 3 = \frac{x}{3} + \frac{1}{3} \cdot - 2$

Step 3.1.5

Combine $\frac{1}{3}$ and $- 2$ .

$y - 3 = \frac{x}{3} + \frac{- 2}{3}$

Step 3.1.6

Move the negative in front of the fraction.

$y - 3 = \frac{x}{3} - \frac{2}{3}$

Step 3.2

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

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Step 3.2.1

Add $3$ to both sides of the equation.

$y = \frac{x}{3} - \frac{2}{3} + 3$

Step 3.2.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{x}{3} - \frac{2}{3} + 3 \cdot \frac{3}{3}$

Step 3.2.3

Combine $3$ and $\frac{3}{3}$ .

$y = \frac{x}{3} - \frac{2}{3} + \frac{3 \cdot 3}{3}$

Step 3.2.4

Combine the numerators over the common denominator.

$y = \frac{x}{3} + \frac{- 2 + 3 \cdot 3}{3}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $3$ by $3$ .

$y = \frac{x}{3} + \frac{- 2 + 9}{3}$

Step 3.2.5.2

Add $- 2$ and $9$ .

$y = \frac{x}{3} + \frac{7}{3}$

Step 3.3

Reorder terms.

$y = \frac{1}{3} x + \frac{7}{3}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = \frac{1}{3} x + \frac{7}{3}$

Point-slope form:

$y - 3 = \frac{1}{3} \cdot (x - 2)$

Step 5

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