Find the Slope and y-intercept r(x)=5x-(2+2x)/3

$r (x) = 5 x - \frac{(2 + 2 x)}{3}$

Step 1

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 $5 x - \frac{2 + 2 x}{3}$ .

Factor $2$ out of $2 + 2 x$ .

Factor $2$ out of $2$ .

$y = 5 x - \frac{2 \cdot 1 + 2 x}{3}$

Factor $2$ out of $2 \cdot 1 + 2 x$ .

$y = 5 x - \frac{2 (1 + x)}{3}$

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = 5 x \cdot \frac{3}{3} - \frac{2 (1 + x)}{3}$

Simplify terms.

Combine $5 x$ and $\frac{3}{3}$ .

$y = \frac{5 x \cdot 3}{3} - \frac{2 (1 + x)}{3}$

Combine the numerators over the common denominator.

$y = \frac{5 x \cdot 3 - 2 (1 + x)}{3}$

Simplify the numerator.

Multiply $3$ by $5$ .

$y = \frac{15 x - 2 (1 + x)}{3}$

Apply the distributive property.

$y = \frac{15 x - 2 \cdot 1 - 2 x}{3}$

Multiply $- 2$ by $1$ .

$y = \frac{15 x - 2 - 2 x}{3}$

Subtract $2 x$ from $15 x$ .

$y = \frac{13 x - 2}{3}$

Simplify $\frac{13 x - 2}{3}$ .

Split the fraction $\frac{13 x - 2}{3}$ into two fractions.

$y = \frac{13 x}{3} + \frac{- 2}{3}$

Move the negative in front of the fraction.

$y = \frac{13 x}{3} - \frac{2}{3}$

Reorder terms.

$y = \frac{13}{3} x - \frac{2}{3}$

Step 2

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

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

$m = \frac{13}{3}$

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

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

Slope: $\frac{13}{3}$

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

Slope: $\frac{13}{3}$

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

Step 3

Find the Slope and y-intercept r(x)=5x-(2+2x)/3

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