Algebra Examples

$q (x) = 4 x - \frac{(3 + 9 x)}{2}$

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 $4 x - \frac{3 + 9 x}{2}$ .

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Step 1.2.1.1

Factor $3$ out of $3 + 9 x$ .

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Step 1.2.1.1.1

Factor $3$ out of $3$ .

$y = 4 x - \frac{3 (1) + 9 x}{2}$

Step 1.2.1.1.2

Factor $3$ out of $9 x$ .

$y = 4 x - \frac{3 (1) + 3 (3 x)}{2}$

Step 1.2.1.1.3

Factor $3$ out of $3 (1) + 3 (3 x)$ .

$y = 4 x - \frac{3 (1 + 3 x)}{2}$

Step 1.2.1.2

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = 4 x \cdot \frac{2}{2} - \frac{3 (1 + 3 x)}{2}$

Step 1.2.1.3

Simplify terms.

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Step 1.2.1.3.1

Combine $4 x$ and $\frac{2}{2}$ .

$y = \frac{4 x \cdot 2}{2} - \frac{3 (1 + 3 x)}{2}$

Step 1.2.1.3.2

Combine the numerators over the common denominator.

$y = \frac{4 x \cdot 2 - 3 (1 + 3 x)}{2}$

Step 1.2.1.4

Simplify the numerator.

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Step 1.2.1.4.1

Multiply $2$ by $4$ .

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

Step 1.2.1.4.2

Apply the distributive property.

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

Step 1.2.1.4.3

Multiply $- 3$ by $1$ .

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

Step 1.2.1.4.4

Multiply $3$ by $- 3$ .

$y = \frac{8 x - 3 - 9 x}{2}$

Step 1.2.1.4.5

Subtract $9 x$ from $8 x$ .

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

Step 1.2.1.5

Simplify with factoring out.

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Step 1.2.1.5.1

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

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

Step 1.2.1.5.2

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

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

Step 1.2.1.5.3

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

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

Step 1.2.1.5.4

Simplify the expression.

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Step 1.2.1.5.4.1

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

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

Step 1.2.1.5.4.2

Move the negative in front of the fraction.

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Apply the distributive property.

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

Step 1.4

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

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Step 1.4.1

Reorder terms.

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

Step 1.4.2

Remove parentheses.

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

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 $y = m x + b$ .

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

$b = - \frac{3}{2}$

Step 2.2

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, - \frac{3}{2})$

Slope: $- \frac{1}{2}$

y-intercept: $(0, - \frac{3}{2})$

Step 3