Find the Slope and y-intercept q(x)=3x-(1+5x)/7

$q (x) = 3 x - \frac{(1 + 5 x)}{7}$

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 $3 x - \frac{1 + 5 x}{7}$ .

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = 3 x \cdot \frac{7}{7} - \frac{1 + 5 x}{7}$

Simplify terms.

Combine $3 x$ and $\frac{7}{7}$ .

$y = \frac{3 x \cdot 7}{7} - \frac{1 + 5 x}{7}$

Combine the numerators over the common denominator.

$y = \frac{3 x \cdot 7 - (1 + 5 x)}{7}$

Simplify the numerator.

Multiply $7$ by $3$ .

$y = \frac{21 x - (1 + 5 x)}{7}$

Apply the distributive property.

$y = \frac{21 x - 1 \cdot 1 - (5 x)}{7}$

Multiply $- 1$ by $1$ .

$y = \frac{21 x - 1 - (5 x)}{7}$

Multiply $5$ by $- 1$ .

$y = \frac{21 x - 1 - 5 x}{7}$

Subtract $5 x$ from $21 x$ .

$y = \frac{16 x - 1}{7}$

Simplify $\frac{16 x - 1}{7}$ .

Split the fraction $\frac{16 x - 1}{7}$ into two fractions.

$y = \frac{16 x}{7} + \frac{- 1}{7}$

Move the negative in front of the fraction.

$y = \frac{16 x}{7} - \frac{1}{7}$

Reorder terms.

$y = \frac{16}{7} x - \frac{1}{7}$

Step 2

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

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

$m = \frac{16}{7}$

$b = - \frac{1}{7}$

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

Slope: $\frac{16}{7}$

y-intercept: $(0, - \frac{1}{7})$

Slope: $\frac{16}{7}$

y-intercept: $(0, - \frac{1}{7})$

Step 3