Find the Slope and y-intercept h(x)=(3x-6)/8

$h (x) = \frac{3 x - 6}{8}$

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.

Factor $3$ out of $3 x - 6$ .

Factor $3$ out of $3 x$ .

$y = \frac{3 (x) - 6}{8}$

Factor $3$ out of $- 6$ .

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

Factor $3$ out of $3 x + 3 \cdot - 2$ .

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

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

Apply the distributive property.

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

Multiply $3$ by $- 2$ .

$y = \frac{3 x - 6}{8}$

Split the fraction $\frac{3 x - 6}{8}$ into two fractions.

$y = \frac{3 x}{8} + \frac{- 6}{8}$

Cancel the common factor of $- 6$ and $8$ .

Factor $2$ out of $- 6$ .

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

Cancel the common factors.

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Reorder terms.

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

Step 2

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

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

$m = \frac{3}{8}$

$b = - \frac{3}{4}$

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

Slope: $\frac{3}{8}$

y-intercept: $(0, - \frac{3}{4})$

Slope: $\frac{3}{8}$

y-intercept: $(0, - \frac{3}{4})$

Step 3