Find the Slope and y-intercept q(x)=5x-(3+4x)/3

$q (x) = 5 x - \frac{(3 + 4 x)}{3}$

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 $5 x - \frac{3 + 4 x}{3}$ .

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

$y = 5 x \cdot \frac{3}{3} - \frac{3 + 4 x}{3}$

Simplify terms.

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

$y = \frac{5 x \cdot 3}{3} - \frac{3 + 4 x}{3}$

Combine the numerators over the common denominator.

$y = \frac{5 x \cdot 3 - (3 + 4 x)}{3}$

Simplify the numerator.

Multiply $3$ by $5$ .

$y = \frac{15 x - (3 + 4 x)}{3}$

Apply the distributive property.

$y = \frac{15 x - 1 \cdot 3 - (4 x)}{3}$

Multiply $- 1$ by $3$ .

$y = \frac{15 x - 3 - (4 x)}{3}$

Multiply $4$ by $- 1$ .

$y = \frac{15 x - 3 - 4 x}{3}$

Subtract $4 x$ from $15 x$ .

$y = \frac{11 x - 3}{3}$

Simplify $\frac{11 x - 3}{3}$ .

Split the fraction $\frac{11 x - 3}{3}$ into two fractions.

$y = \frac{11 x}{3} + \frac{- 3}{3}$

Divide $- 3$ by $3$ .

$y = \frac{11 x}{3} - 1$

Reorder terms.

$y = \frac{11}{3} x - 1$

Step 2

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

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

$m = \frac{11}{3}$

$b = - 1$

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

Slope: $\frac{11}{3}$

y-intercept: $(0, - 1)$

Slope: $\frac{11}{3}$

y-intercept: $(0, - 1)$

Step 3