Algebra Examples

$q (x) = x - \frac{(3 + 8 x)}{6}$

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

Simplify the right side.

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Step 1.2.1

Simplify $x - \frac{3 + 8 x}{6}$ .

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Step 1.2.1.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

Step 1.2.1.2

Simplify terms.

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Step 1.2.1.2.1

Combine $x$ and $\frac{6}{6}$ .

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

Step 1.2.1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.1.3

Simplify the numerator.

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Step 1.2.1.3.1

Move $6$ to the left of $x$ .

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

Step 1.2.1.3.2

Apply the distributive property.

$y = \frac{6 x - 1 \cdot 3 - (8 x)}{6}$

Step 1.2.1.3.3

Multiply $- 1$ by $3$ .

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

Step 1.2.1.3.4

Multiply $8$ by $- 1$ .

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

Step 1.2.1.3.5

Subtract $8 x$ from $6 x$ .

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

Step 1.2.1.4

Simplify with factoring out.

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Step 1.2.1.4.1

Factor $- 1$ out of $- 2 x$ .

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

Step 1.2.1.4.2

Rewrite $- 3$ as $- 1 (3)$ .

$y = \frac{- (2 x) - 1 (3)}{6}$

Step 1.2.1.4.3

Factor $- 1$ out of $- (2 x) - 1 (3)$ .

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

Step 1.2.1.4.4

Simplify the expression.

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Step 1.2.1.4.4.1

Rewrite $- (2 x + 3)$ as $- 1 (2 x + 3)$ .

$y = \frac{- 1 (2 x + 3)}{6}$

Step 1.2.1.4.4.2

Move the negative in front of the fraction.

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

Step 1.3

Simplify $- \frac{2 x + 3}{6}$ .

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Step 1.3.1

Split the fraction $\frac{2 x + 3}{6}$ into two fractions.

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

Step 1.3.2

Simplify each term.

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Step 1.3.2.1

Cancel the common factor of $2$ and $6$ .

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Step 1.3.2.1.1

Factor $2$ out of $2 x$ .

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

Step 1.3.2.1.2

Cancel the common factors.

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Step 1.3.2.1.2.1

Factor $2$ out of $6$ .

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

Step 1.3.2.1.2.2

Cancel the common factor.

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

Step 1.3.2.1.2.3

Rewrite the expression.

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

Step 1.3.2.2

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

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Step 1.3.2.2.1

Factor $3$ out of $3$ .

$y = - (\frac{x}{3} + \frac{3 (1)}{6})$

Step 1.3.2.2.2

Cancel the common factors.

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Step 1.3.2.2.2.1

Factor $3$ out of $6$ .

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

Step 1.3.2.2.2.2

Cancel the common factor.

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

Step 1.3.2.2.2.3

Rewrite the expression.

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

Step 1.3.3

Apply the distributive property.

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

Step 1.4

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

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Step 1.4.1

Reorder terms.

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

Step 1.4.2

Remove parentheses.

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

Step 2

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

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Step 2.1

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

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

$b = - \frac{1}{2}$

Step 2.2

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

Slope: $- \frac{1}{3}$

y-intercept: $(0, - \frac{1}{2})$

Slope: $- \frac{1}{3}$

y-intercept: $(0, - \frac{1}{2})$

Step 3