Question

graph the function.
$f(x)=\frac{1}{4}x + 6$
use the graphing tool on the right to graph the function.
click to enlarge graph

Explanation:

Step1: Identify the slope and y-intercept

The function \( f(x) = \frac{1}{4}x + 6 \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{1}{4} \) (slope) and \( b = 6 \) (y - intercept).

Step2: Plot the y - intercept

The y - intercept is \( (0,6) \). So we plot the point \( (0,6) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{1}{4}=\frac{\text{rise}}{\text{run}} \). From the point \( (0,6) \), we move up 1 unit (rise) and then 4 units to the right (run). This gives us the point \( (0 + 4,6+1)=(4,7) \). We can also move down 1 unit and 4 units to the left from \( (0,6) \) to get the point \( (0 - 4,6 - 1)=(-4,5) \).

Step4: Draw the line

Draw a straight line passing through the points we found (e.g., \( (0,6) \), \( (4,7) \), \( (-4,5) \)) to graph the function \( f(x)=\frac{1}{4}x + 6 \).

(Note: Since the problem asks to use the graphing tool, the above steps are for the manual graphing process. If using a graphing tool, we can input the function \( y=\frac{1}{4}x + 6 \) and the tool will plot the line with a slope of \( \frac{1}{4} \) and y - intercept at \( (0,6) \).)

Answer:

The graph of \( f(x)=\frac{1}{4}x + 6 \) is a straight line with y - intercept at \( (0,6) \) and a slope of \( \frac{1}{4} \). When using the graphing tool, input the function \( y=\frac{1}{4}x + 6 \) to obtain the graph.