Find the Slope and y-intercept q(x)=5x-(3+2x)/6

$q (x) = 5 x - \frac{(3 + 2 x)}{6}$

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 $5 x - \frac{3 + 2 x}{6}$ .

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = 5 x \cdot \frac{6}{6} - \frac{3 + 2 x}{6}$

Simplify terms.

Combine $5 x$ and $\frac{6}{6}$ .

$y = \frac{5 x \cdot 6}{6} - \frac{3 + 2 x}{6}$

Combine the numerators over the common denominator.

$y = \frac{5 x \cdot 6 - (3 + 2 x)}{6}$

Simplify the numerator.

Multiply $6$ by $5$ .

$y = \frac{30 x - (3 + 2 x)}{6}$

Apply the distributive property.

$y = \frac{30 x - 1 \cdot 3 - (2 x)}{6}$

Multiply $- 1$ by $3$ .

$y = \frac{30 x - 3 - (2 x)}{6}$

Multiply $2$ by $- 1$ .

$y = \frac{30 x - 3 - 2 x}{6}$

Subtract $2 x$ from $30 x$ .

$y = \frac{28 x - 3}{6}$

Simplify $\frac{28 x - 3}{6}$ .

Split the fraction $\frac{28 x - 3}{6}$ into two fractions.

$y = \frac{28 x}{6} + \frac{- 3}{6}$

Simplify each term.

Cancel the common factor of $28$ and $6$ .

Factor $2$ out of $28 x$ .

$y = \frac{2 (14 x)}{6} + \frac{- 3}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$y = \frac{2 (14 x)}{2 (3)} + \frac{- 3}{6}$

Cancel the common factor.

$y = \frac{2 (14 x)}{2 \cdot 3} + \frac{- 3}{6}$

Rewrite the expression.

$y = \frac{14 x}{3} + \frac{- 3}{6}$

Cancel the common factor of $- 3$ and $6$ .

Factor $3$ out of $- 3$ .

$y = \frac{14 x}{3} + \frac{3 (- 1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$y = \frac{14 x}{3} + \frac{3 \cdot - 1}{3 \cdot 2}$

Cancel the common factor.

$y = \frac{14 x}{3} + \frac{3 \cdot - 1}{3 \cdot 2}$

Rewrite the expression.

$y = \frac{14 x}{3} + \frac{- 1}{2}$

Move the negative in front of the fraction.

$y = \frac{14 x}{3} - \frac{1}{2}$

Reorder terms.

$y = \frac{14}{3} x - \frac{1}{2}$

Step 2

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

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

$m = \frac{14}{3}$

$b = - \frac{1}{2}$

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

Slope: $\frac{14}{3}$

y-intercept: $(0, - \frac{1}{2})$

Slope: $\frac{14}{3}$

y-intercept: $(0, - \frac{1}{2})$

Step 3

Find the Slope and y-intercept q(x)=5x-(3+2x)/6

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