Pre-Algebra Examples

$6 x - 3 y = 8$

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 $6 x$ from both sides of the equation.

$- 3 y = 8 - 6 x$

Step 1.3

Divide each term in $- 3 y = 8 - 6 x$ by $- 3$ and simplify.

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Step 1.3.1

Divide each term in $- 3 y = 8 - 6 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{8}{- 3} + \frac{- 6 x}{- 3}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 3$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{8}{- 3} + \frac{- 6 x}{- 3}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{- 3} + \frac{- 6 x}{- 3}$

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

Move the negative in front of the fraction.

$y = - \frac{8}{3} + \frac{- 6 x}{- 3}$

Step 1.3.3.1.2

Cancel the common factor of $- 6$ and $- 3$ .

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Step 1.3.3.1.2.1

Factor $- 3$ out of $- 6 x$ .

$y = - \frac{8}{3} + \frac{- 3 (2 x)}{- 3}$

Step 1.3.3.1.2.2

Cancel the common factors.

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Step 1.3.3.1.2.2.1

Factor $- 3$ out of $- 3$ .

$y = - \frac{8}{3} + \frac{- 3 (2 x)}{- 3 (1)}$

Step 1.3.3.1.2.2.2

Cancel the common factor.

$y = - \frac{8}{3} + \frac{- 3 (2 x)}{- 3 \cdot 1}$

Step 1.3.3.1.2.2.3

Rewrite the expression.

$y = - \frac{8}{3} + \frac{2 x}{1}$

Step 1.3.3.1.2.2.4

Divide $2 x$ by $1$ .

$y = - \frac{8}{3} + 2 x$

Step 1.4

Reorder $- \frac{8}{3}$ and $2 x$ .

$y = 2 x - \frac{8}{3}$

Step 2

Using the slope-intercept form, the y-intercept is $- \frac{8}{3}$ .

$b = - \frac{8}{3}$

Step 3

y-intercept in point form.

$(0, - \frac{8}{3})$

Step 4