Find the Slope and y-intercept r(x)=(6x-4)/7

$r (x) = \frac{6 x - 4}{7}$

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.

Factor $2$ out of $6 x - 4$ .

Factor $2$ out of $6 x$ .

$y = \frac{2 (3 x) - 4}{7}$

Factor $2$ out of $- 4$ .

$y = \frac{2 (3 x) + 2 (- 2)}{7}$

Factor $2$ out of $2 (3 x) + 2 (- 2)$ .

$y = \frac{2 (3 x - 2)}{7}$

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

Apply the distributive property.

$y = \frac{2 (3 x) + 2 \cdot - 2}{7}$

Multiply $3$ by $2$ .

$y = \frac{6 x + 2 \cdot - 2}{7}$

Multiply $2$ by $- 2$ .

$y = \frac{6 x - 4}{7}$

Split the fraction $\frac{6 x - 4}{7}$ into two fractions.

$y = \frac{6 x}{7} + \frac{- 4}{7}$

Move the negative in front of the fraction.

$y = \frac{6 x}{7} - \frac{4}{7}$

Reorder terms.

$y = \frac{6}{7} x - \frac{4}{7}$

Step 2

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

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

$m = \frac{6}{7}$

$b = - \frac{4}{7}$

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

Slope: $\frac{6}{7}$

y-intercept: $(0, - \frac{4}{7})$

Slope: $\frac{6}{7}$

y-intercept: $(0, - \frac{4}{7})$

Step 3