Algebra Examples

$f (x) = 2 x - \frac{(3 + 7 x)}{4}$

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 $2 x - \frac{3 + 7 x}{4}$ .

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Step 1.2.1.1

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

$y = 2 x \cdot \frac{4}{4} - \frac{3 + 7 x}{4}$

Step 1.2.1.2

Simplify terms.

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Step 1.2.1.2.1

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

$y = \frac{2 x \cdot 4}{4} - \frac{3 + 7 x}{4}$

Step 1.2.1.2.2

Combine the numerators over the common denominator.

$y = \frac{2 x \cdot 4 - (3 + 7 x)}{4}$

Step 1.2.1.3

Simplify the numerator.

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Step 1.2.1.3.1

Multiply $4$ by $2$ .

$y = \frac{8 x - (3 + 7 x)}{4}$

Step 1.2.1.3.2

Apply the distributive property.

$y = \frac{8 x - 1 \cdot 3 - (7 x)}{4}$

Step 1.2.1.3.3

Multiply $- 1$ by $3$ .

$y = \frac{8 x - 3 - (7 x)}{4}$

Step 1.2.1.3.4

Multiply $7$ by $- 1$ .

$y = \frac{8 x - 3 - 7 x}{4}$

Step 1.2.1.3.5

Subtract $7 x$ from $8 x$ .

$y = \frac{x - 3}{4}$

Step 1.3

Simplify $\frac{x - 3}{4}$ .

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Step 1.3.1

Split the fraction $\frac{x - 3}{4}$ into two fractions.

$y = \frac{x}{4} + \frac{- 3}{4}$

Step 1.3.2

Move the negative in front of the fraction.

$y = \frac{x}{4} - \frac{3}{4}$

Step 1.4

Reorder terms.

$y = \frac{1}{4} x - \frac{3}{4}$

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 $y = m x + b$ .

$m = \frac{1}{4}$

$b = - \frac{3}{4}$

Step 2.2

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

Slope: $\frac{1}{4}$

y-intercept: $(0, - \frac{3}{4})$

Slope: $\frac{1}{4}$

y-intercept: $(0, - \frac{3}{4})$

Step 3