Find the Slope and y-intercept q(x)=2x-(2+9x)/5

$q (x) = 2 x - \frac{(2 + 9 x)}{5}$

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 $2 x - \frac{2 + 9 x}{5}$ .

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = 2 x \cdot \frac{5}{5} - \frac{2 + 9 x}{5}$

Simplify terms.

Combine $2 x$ and $\frac{5}{5}$ .

$y = \frac{2 x \cdot 5}{5} - \frac{2 + 9 x}{5}$

Combine the numerators over the common denominator.

$y = \frac{2 x \cdot 5 - (2 + 9 x)}{5}$

Simplify the numerator.

Multiply $5$ by $2$ .

$y = \frac{10 x - (2 + 9 x)}{5}$

Apply the distributive property.

$y = \frac{10 x - 1 \cdot 2 - (9 x)}{5}$

Multiply $- 1$ by $2$ .

$y = \frac{10 x - 2 - (9 x)}{5}$

Multiply $9$ by $- 1$ .

$y = \frac{10 x - 2 - 9 x}{5}$

Subtract $9 x$ from $10 x$ .

$y = \frac{x - 2}{5}$

Simplify $\frac{x - 2}{5}$ .

Split the fraction $\frac{x - 2}{5}$ into two fractions.

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

Move the negative in front of the fraction.

$y = \frac{x}{5} - \frac{2}{5}$

Reorder terms.

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

Step 2

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

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

$m = \frac{1}{5}$

$b = - \frac{2}{5}$

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

Slope: $\frac{1}{5}$

y-intercept: $(0, - \frac{2}{5})$

Slope: $\frac{1}{5}$

y-intercept: $(0, - \frac{2}{5})$

Step 3