Question

graph the linear equation.
$f(x)=\frac{1}{2}x + 2$
use the graphing tool to graph the linear equation.
(click to enlarge graph)

Explanation:

Step1: Identify the slope and y-intercept

The equation \( f(x)=\frac{1}{2}x + 2 \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{1}{2} \) (slope) and \( b = 2 \) (y - intercept).

Step2: Plot the y - intercept

The y - intercept is \( (0,2) \). So we plot the point \( (0,2) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{1}{2}=\frac{\text{rise}}{\text{run}} \). From the point \( (0,2) \), we rise 1 unit (move up 1) and run 2 units (move to the right 2). This gives us the point \( (0 + 2,2+1)=(2,3) \). We can also go in the opposite direction: from \( (0,2) \), rise - 1 (move down 1) and run - 2 (move to the left 2) to get the point \( (0-2,2 - 1)=(-2,1) \).

Step4: Draw the line

Draw a straight line through the points \( (0,2) \), \( (2,3) \), \( (-2,1) \) (or other points found using the slope) to graph the linear equation \( f(x)=\frac{1}{2}x + 2 \).

Answer:

The graph of \( f(x)=\frac{1}{2}x + 2 \) is a straight line with y - intercept at \( (0,2) \) and passing through points like \( (2,3) \) and \( (-2,1) \) (the line is drawn through these points on the given coordinate grid).