Precalculus Examples

m = \frac{1}{3}

$m = \frac{1}{3}$ ,

(2, 3)

$(2, 3)$

Step 1

Use the slope

\frac{1}{3}

$\frac{1}{3}$ and a given point

(2, 3)

$(2, 3)$ to substitute for

x_{1}

$x_{1}$ and

y_{1}

$y_{1}$ in the point-slope form

y - y_{1} = m (x - x_{1})

$y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

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

Step 2

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

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

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

Step 3

Solve for

y

$y$ .

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Step 3.1

Simplify

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

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

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Step 3.1.1

Rewrite.

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

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

Step 3.1.2

Simplify by adding zeros.

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

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

Step 3.1.3

Apply the distributive property.

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

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

Step 3.1.4

Combine

\frac{1}{3}

$\frac{1}{3}$ and

x

$x$ .

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

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

Step 3.1.5

Combine

\frac{1}{3}

$\frac{1}{3}$ and

- 2

$- 2$ .

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

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

Step 3.1.6

Move the negative in front of the fraction.

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

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

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

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

Step 3.2

Move all terms not containing

y

$y$ to the right side of the equation.

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Step 3.2.1

Add

3

$3$ to both sides of the equation.

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

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

Step 3.2.2

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 3.2.3

Combine

3

$3$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply

3

$3$ by

3

$3$ .

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

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

Step 3.2.5.2

Add

- 2

$- 2$ and

9

$9$ .

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

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

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

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

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

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

Step 3.3

Reorder terms.

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

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

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

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

Step 4

List the equation in different forms.

Slope-intercept form:

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

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

Point-slope form:

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

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

Step 5

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