Question

b) $f(x) = 3 - \frac{1}{2}x$

Explanation:

Step1: Identify the function type

The function \( f(x) = 3 - \frac{1}{2}x \) is a linear function in the form \( y = mx + b \), where \( m = -\frac{1}{2} \) (slope) and \( b = 3 \) (y - intercept).

Step2: Find two points on the line

• When \( x = 0 \), \( f(0)=3-\frac{1}{2}(0) = 3 \). So the point is \( (0, 3) \).
• When \( y = 0 \), solve \( 0 = 3-\frac{1}{2}x \).
• Add \( \frac{1}{2}x \) to both sides: \( \frac{1}{2}x=3 \).
• Multiply both sides by 2: \( x = 6 \). So the point is \( (6, 0) \).

Step3: Plot the points and draw the line

Plot the points \( (0, 3) \) and \( (6, 0) \) on the coordinate plane and draw a straight line passing through them.

Answer:

To graph \( f(x)=3 - \frac{1}{2}x \):

1. Plot the y - intercept \( (0, 3) \) (since when \( x = 0 \), \( f(0)=3 \)).
2. Plot the x - intercept \( (6, 0) \) (found by solving \( 0 = 3-\frac{1}{2}x \) to get \( x = 6 \)).
3. Draw a straight line through these two points. The line has a slope of \( -\frac{1}{2} \), meaning for every 2 units you move to the right along the x - axis, you move down 1 unit along the y - axis.