Pre-Algebra Examples

$6 x = - 21 y + 42$

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

Rewrite the equation as $- 21 y + 42 = 6 x$ .

$- 21 y + 42 = 6 x$

Step 1.3

Subtract $42$ from both sides of the equation.

$- 21 y = 6 x - 42$

Step 1.4

Divide each term in $- 21 y = 6 x - 42$ by $- 21$ and simplify.

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Step 1.4.1

Divide each term in $- 21 y = 6 x - 42$ by $- 21$ .

$\frac{- 21 y}{- 21} = \frac{6 x}{- 21} + \frac{- 42}{- 21}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $- 21$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{- 21 y}{- 21} = \frac{6 x}{- 21} + \frac{- 42}{- 21}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{6 x}{- 21} + \frac{- 42}{- 21}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

Cancel the common factor of $6$ and $- 21$ .

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Step 1.4.3.1.1.1

Factor $3$ out of $6 x$ .

$y = \frac{3 (2 x)}{- 21} + \frac{- 42}{- 21}$

Step 1.4.3.1.1.2

Cancel the common factors.

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Step 1.4.3.1.1.2.1

Factor $3$ out of $- 21$ .

$y = \frac{3 (2 x)}{3 (- 7)} + \frac{- 42}{- 21}$

Step 1.4.3.1.1.2.2

Cancel the common factor.

$y = \frac{3 (2 x)}{3 \cdot - 7} + \frac{- 42}{- 21}$

Step 1.4.3.1.1.2.3

Rewrite the expression.

$y = \frac{2 x}{- 7} + \frac{- 42}{- 21}$

Step 1.4.3.1.2

Move the negative in front of the fraction.

$y = - \frac{2 x}{7} + \frac{- 42}{- 21}$

Step 1.4.3.1.3

Divide $- 42$ by $- 21$ .

$y = - \frac{2 x}{7} + 2$

Step 1.5

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

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Step 1.5.1

Reorder terms.

$y = - (\frac{2}{7} x) + 2$

Step 1.5.2

Remove parentheses.

$y = - \frac{2}{7} x + 2$

Step 2

Using the slope-intercept form, the y-intercept is $2$ .

$b = 2$

Step 3

y-intercept in point form.

$(0, 2)$

Step 4