Find the Slope and y-intercept q(x)=3x-(4+7x)/8

$q (x) = 3 x - \frac{(4 + 7 x)}{8}$

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 $3 x - \frac{4 + 7 x}{8}$ .

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y = 3 x \cdot \frac{8}{8} - \frac{4 + 7 x}{8}$

Simplify terms.

Combine $3 x$ and $\frac{8}{8}$ .

$y = \frac{3 x \cdot 8}{8} - \frac{4 + 7 x}{8}$

Combine the numerators over the common denominator.

$y = \frac{3 x \cdot 8 - (4 + 7 x)}{8}$

Simplify the numerator.

Multiply $8$ by $3$ .

$y = \frac{24 x - (4 + 7 x)}{8}$

Apply the distributive property.

$y = \frac{24 x - 1 \cdot 4 - (7 x)}{8}$

Multiply $- 1$ by $4$ .

$y = \frac{24 x - 4 - (7 x)}{8}$

Multiply $7$ by $- 1$ .

$y = \frac{24 x - 4 - 7 x}{8}$

Subtract $7 x$ from $24 x$ .

$y = \frac{17 x - 4}{8}$

Simplify $\frac{17 x - 4}{8}$ .

Split the fraction $\frac{17 x - 4}{8}$ into two fractions.

$y = \frac{17 x}{8} + \frac{- 4}{8}$

Simplify each term.

Cancel the common factor of $- 4$ and $8$ .

Factor $4$ out of $- 4$ .

$y = \frac{17 x}{8} + \frac{4 (- 1)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$y = \frac{17 x}{8} + \frac{4 \cdot - 1}{4 \cdot 2}$

Cancel the common factor.

$y = \frac{17 x}{8} + \frac{4 \cdot - 1}{4 \cdot 2}$

Rewrite the expression.

$y = \frac{17 x}{8} + \frac{- 1}{2}$

Move the negative in front of the fraction.

$y = \frac{17 x}{8} - \frac{1}{2}$

Reorder terms.

$y = \frac{17}{8} x - \frac{1}{2}$

Step 2

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

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

$m = \frac{17}{8}$

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

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

Slope: $\frac{17}{8}$

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

Slope: $\frac{17}{8}$

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

Step 3

Find the Slope and y-intercept q(x)=3x-(4+7x)/8

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