Find the Slope and y-intercept q(x)=5x-(3+4x)/8

$q (x) = 5 x - \frac{(3 + 4 x)}{8}$

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 $5 x - \frac{3 + 4 x}{8}$ .

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y = 5 x \cdot \frac{8}{8} - \frac{3 + 4 x}{8}$

Simplify terms.

Combine $5 x$ and $\frac{8}{8}$ .

$y = \frac{5 x \cdot 8}{8} - \frac{3 + 4 x}{8}$

Combine the numerators over the common denominator.

$y = \frac{5 x \cdot 8 - (3 + 4 x)}{8}$

Simplify the numerator.

Multiply $8$ by $5$ .

$y = \frac{40 x - (3 + 4 x)}{8}$

Apply the distributive property.

$y = \frac{40 x - 1 \cdot 3 - (4 x)}{8}$

Multiply $- 1$ by $3$ .

$y = \frac{40 x - 3 - (4 x)}{8}$

Multiply $4$ by $- 1$ .

$y = \frac{40 x - 3 - 4 x}{8}$

Subtract $4 x$ from $40 x$ .

$y = \frac{36 x - 3}{8}$

Factor $3$ out of $36 x - 3$ .

Factor $3$ out of $36 x$ .

$y = \frac{3 (12 x) - 3}{8}$

Factor $3$ out of $- 3$ .

$y = \frac{3 (12 x) + 3 (- 1)}{8}$

Factor $3$ out of $3 (12 x) + 3 (- 1)$ .

$y = \frac{3 (12 x - 1)}{8}$

Write in $y = m x + b$ form.

Apply the distributive property.

$y = \frac{3 (12 x) + 3 \cdot - 1}{8}$

Multiply $12$ by $3$ .

$y = \frac{36 x + 3 \cdot - 1}{8}$

Multiply $3$ by $- 1$ .

$y = \frac{36 x - 3}{8}$

Split the fraction $\frac{36 x - 3}{8}$ into two fractions.

$y = \frac{36 x}{8} + \frac{- 3}{8}$

Cancel the common factor of $36$ and $8$ .

Factor $4$ out of $36 x$ .

$y = \frac{4 (9 x)}{8} + \frac{- 3}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$y = \frac{4 (9 x)}{4 (2)} + \frac{- 3}{8}$

Cancel the common factor.

$y = \frac{4 (9 x)}{4 \cdot 2} + \frac{- 3}{8}$

Rewrite the expression.

$y = \frac{9 x}{2} + \frac{- 3}{8}$

Move the negative in front of the fraction.

$y = \frac{9 x}{2} - \frac{3}{8}$

Reorder terms.

$y = \frac{9}{2} x - \frac{3}{8}$

Step 2

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

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

$m = \frac{9}{2}$

$b = - \frac{3}{8}$

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

Slope: $\frac{9}{2}$

y-intercept: $(0, - \frac{3}{8})$

Slope: $\frac{9}{2}$

y-intercept: $(0, - \frac{3}{8})$

Step 3

Find the Slope and y-intercept q(x)=5x-(3+4x)/8

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