Question

Which graph best represents the function f(x) = - 1/4x + 5?

Answer 1

To represent the function \( f(x) = -\frac{1}{4}x + 5 \) graphically, we need to recognize that it is a linear equation in slope-intercept form, \( y = mx + b \), where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

In this case:
- The slope \( m = -\frac{1}{4} \) means the line decreases as \( x \) increases. For every 4 units you move to the right (in the positive x-direction), the value of \( f(x) \) will decrease by 1 unit.
- The y-intercept \( b = 5 \) indicates that the line crosses the y-axis at the point (0, 5).

To graph this function:
1. Start at the point (0, 5) on the y-axis.
2. From that point, move right 4 units (to x = 4) and down 1 unit (to y = 4), to get another point on the line (4, 4).
3. Draw a line through these points extending in both directions.

In summary, the graph of \( f(x) = -\frac{1}{4}x + 5 \) will be a straight line that slopes downward from left to right, crosses the y-axis at 5, and has a gentle slope of -1/4. If you have multiple graph options, look for the one that illustrates this behavior.