Graph r(x)=(x^2+6x+8)/(2x+8)

$r (x) = \frac{x^{2} + 6 x + 8}{2 x + 8}$

Rewrite the function as an equation.

$y = \frac{x + 2}{2}$

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 $\frac{x + 2}{2}$ .

Split the fraction $\frac{x + 2}{2}$ into two fractions.

$y = \frac{x}{2} + \frac{2}{2}$

Divide $2$ by $2$ .

$y = \frac{x}{2} + 1$

Reorder terms.

$y = \frac{1}{2} x + 1$

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

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

$m = \frac{1}{2}$

$b = 1$

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

Slope: $\frac{1}{2}$

y-intercept: $(0, 1)$

Slope: $\frac{1}{2}$

y-intercept: $(0, 1)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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

Split the fraction $\frac{x + 2}{2}$ into two fractions.

$y = \frac{x}{2} + \frac{2}{2}$

Divide $2$ by $2$ .

$y = \frac{x}{2} + 1$

Reorder terms.

$y = \frac{1}{2} x + 1$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 1 \\ 2 & 2 \end{array}$

Graph the line using the slope and the y-intercept, or the points.

Slope: $\frac{1}{2}$

y-intercept: $(0, 1)$

$\begin{array}{c} x & y \\ 0 & 1 \\ 2 & 2 \end{array}$