Find the Slope and y-intercept q(x)=4x-(1+3x)/8

$q (x) = 4 x - \frac{(1 + 3 x)}{8}$

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 $4 x - \frac{1 + 3 x}{8}$ .

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y = 4 x \cdot \frac{8}{8} - \frac{1 + 3 x}{8}$

Simplify terms.

Combine $4 x$ and $\frac{8}{8}$ .

$y = \frac{4 x \cdot 8}{8} - \frac{1 + 3 x}{8}$

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $8$ by $4$ .

$y = \frac{32 x - (1 + 3 x)}{8}$

Apply the distributive property.

$y = \frac{32 x - 1 \cdot 1 - (3 x)}{8}$

Multiply $- 1$ by $1$ .

$y = \frac{32 x - 1 - (3 x)}{8}$

Multiply $3$ by $- 1$ .

$y = \frac{32 x - 1 - 3 x}{8}$

Subtract $3 x$ from $32 x$ .

$y = \frac{29 x - 1}{8}$

Simplify $\frac{29 x - 1}{8}$ .

Split the fraction $\frac{29 x - 1}{8}$ into two fractions.

$y = \frac{29 x}{8} + \frac{- 1}{8}$

Move the negative in front of the fraction.

$y = \frac{29 x}{8} - \frac{1}{8}$

Reorder terms.

$y = \frac{29}{8} x - \frac{1}{8}$

Step 2

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

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

$m = \frac{29}{8}$

$b = - \frac{1}{8}$

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

Slope: $\frac{29}{8}$

y-intercept: $(0, - \frac{1}{8})$

Slope: $\frac{29}{8}$

y-intercept: $(0, - \frac{1}{8})$

Step 3