Pre-Algebra Examples

$3 x + 2 y = - 12$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Subtract $3 x$ from both sides of the equation.

$2 y = - 12 - 3 x$

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $2$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide $y$ by $1$ .

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

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide $- 12$ by $2$ .

$y = - 6 + \frac{- 3 x}{2}$

Step 1.3.3.1.2

Move the negative in front of the fraction.

$y = - 6 - \frac{3 x}{2}$

Step 1.4

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

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Step 1.4.1

Reorder $- 6$ and $- \frac{3 x}{2}$ .

$y = - \frac{3 x}{2} - 6$

Step 1.4.2

Reorder terms.

$y = - (\frac{3}{2} x) - 6$

Step 1.4.3

Remove parentheses.

$y = - \frac{3}{2} x - 6$

Step 2

Using the slope-intercept form, the y-intercept is $- 6$ .

$b = - 6$

Step 3

y-intercept in point form.

$(0, - 6)$

Step 4