Precalculus Examples

$2 x - 3 y = 12$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $2 x$ from both sides of the equation.

$- 3 y = 12 - 2 x$

Step 1.2

Divide each term in $- 3 y = 12 - 2 x$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 y = 12 - 2 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{12}{- 3} + \frac{- 2 x}{- 3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{12}{- 3} + \frac{- 2 x}{- 3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{- 3} + \frac{- 2 x}{- 3}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $12$ by $- 3$ .

$y = - 4 + \frac{- 2 x}{- 3}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = - 4 + \frac{2 x}{3}$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2

Reorder $- 4$ and $\frac{2 x}{3}$ .

$y = \frac{2 x}{3} - 4$

Step 2.3

Reorder terms.

$y = \frac{2}{3} x - 4$

Step 3

Use the slope-intercept form to find the slope and y-intercept.

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Step 3.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{2}{3}$

$b = - 4$

Step 3.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{2}{3}$

y-intercept: $(0, - 4)$

Slope: $\frac{2}{3}$

y-intercept: $(0, - 4)$

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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Step 4.1

Write in $y = m x + b$ form.

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Step 4.1.1

Reorder $- 4$ and $\frac{2 x}{3}$ .

$y = \frac{2 x}{3} - 4$

Step 4.1.2

Reorder terms.

$y = \frac{2}{3} x - 4$

Step 4.2

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & - 4 \\ 3 & - 2 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope: $\frac{2}{3}$

y-intercept: $(0, - 4)$

$\begin{array}{c} x & y \\ 0 & - 4 \\ 3 & - 2 \end{array}$

Step 6