Find the Slope and y-intercept f(x)=2(1-1/3x)+4x

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

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Simplify the right side.

Simplify $2 (1 - \frac{1}{3} x) + 4 x$ .

Simplify each term.

Combine $x$ and $\frac{1}{3}$ .

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

Apply the distributive property.

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

Multiply $2$ by $1$ .

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

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

Multiply $- 1$ by $2$ .

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

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

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

Move the negative in front of the fraction.

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

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Simplify terms.

Combine $4 x$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $2 x$ out of $- 2 x + 4 x \cdot 3$ .

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

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

Factor $2 x$ out of $4 x \cdot 3$ .

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

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

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

Multiply $2$ by $3$ .

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

Add $- 1$ and $6$ .

$y = 2 + \frac{2 x \cdot 5}{3}$

Multiply $5$ by $2$ .

$y = 2 + \frac{10 x}{3}$

Reorder $2$ and $\frac{10 x}{3}$ .

$y = \frac{10 x}{3} + 2$

Reorder terms.

$y = \frac{10}{3} x + 2$

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

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

$m = \frac{10}{3}$

$b = 2$

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

Slope: $\frac{10}{3}$

y-intercept: $(0, 2)$

Slope: $\frac{10}{3}$

y-intercept: $(0, 2)$

Find the Slope and y-intercept f(x)=2(1-1/3x)+4x

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