Algebra Examples

$f (x) = 2 (1 - \frac{8}{3} x) + 6 x$

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 $2 (1 - \frac{8}{3} x) + 6 x$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Simplify each term.

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Step 1.2.1.1.1.1

Combine $x$ and $\frac{8}{3}$ .

$y = 2 (1 - \frac{x \cdot 8}{3}) + 6 x$

Step 1.2.1.1.1.2

Move $8$ to the left of $x$ .

$y = 2 (1 - \frac{8 x}{3}) + 6 x$

Step 1.2.1.1.2

Apply the distributive property.

$y = 2 \cdot 1 + 2 (- \frac{8 x}{3}) + 6 x$

Step 1.2.1.1.3

Multiply $2$ by $1$ .

$y = 2 + 2 (- \frac{8 x}{3}) + 6 x$

Step 1.2.1.1.4

Multiply $2 (- \frac{8 x}{3})$ .

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Step 1.2.1.1.4.1

Multiply $- 1$ by $2$ .

$y = 2 - 2 \frac{8 x}{3} + 6 x$

Step 1.2.1.1.4.2

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

$y = 2 + \frac{- 2 (8 x)}{3} + 6 x$

Step 1.2.1.1.4.3

Multiply $8$ by $- 2$ .

$y = 2 + \frac{- 16 x}{3} + 6 x$

Step 1.2.1.1.5

Move the negative in front of the fraction.

$y = 2 - \frac{16 x}{3} + 6 x$

Step 1.2.1.2

To write $6 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = 2 - \frac{16 x}{3} + 6 x \cdot \frac{3}{3}$

Step 1.2.1.3

Simplify terms.

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Step 1.2.1.3.1

Combine $6 x$ and $\frac{3}{3}$ .

$y = 2 - \frac{16 x}{3} + \frac{6 x \cdot 3}{3}$

Step 1.2.1.3.2

Combine the numerators over the common denominator.

$y = 2 + \frac{- 16 x + 6 x \cdot 3}{3}$

Step 1.2.1.4

Simplify the numerator.

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Step 1.2.1.4.1

Factor $2 x$ out of $- 16 x + 6 x \cdot 3$ .

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Step 1.2.1.4.1.1

Factor $2 x$ out of $- 16 x$ .

$y = 2 + \frac{2 x (- 8) + 6 x \cdot 3}{3}$

Step 1.2.1.4.1.2

Factor $2 x$ out of $6 x \cdot 3$ .

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

Step 1.2.1.4.1.3

Factor $2 x$ out of $2 x (- 8) + 2 x (3 \cdot 3)$ .

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

Step 1.2.1.4.2

Multiply $3$ by $3$ .

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

Step 1.2.1.4.3

Add $- 8$ and $9$ .

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

Step 1.2.1.4.4

Multiply $2$ by $1$ .

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

Step 1.3

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

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

Step 1.4

Reorder terms.

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

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 $y = m x + b$ .

$m = \frac{2}{3}$

$b = 2$

Step 2.2

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

Slope: $\frac{2}{3}$

y-intercept: $(0, 2)$

Slope: $\frac{2}{3}$

y-intercept: $(0, 2)$

Step 3