Question

which graphs show functions with direct variation? select three options.
parking garage rates
total cost ($)
time (hours)
(1, 2.4)
(5, 4)
cost of cinnamon
total cost ($)

Explanation:

Step1: Recall Direct Variation

A direct variation function has the form \( y = kx \), where \( k \) is a constant, and the graph passes through the origin \((0,0)\) (since when \( x = 0 \), \( y = 0 \)).

Step2: Analyze First Graph

The first graph (Parking Garage Rates) has a y - intercept at \( y = 2 \) (when \( x = 0 \), \( y = 2 \)), so it does not pass through the origin. Thus, it is not a direct variation.

Step3: Analyze Second Graph (Cost of Cinnamon)

Wait, the second graph's visible part: if we assume (but since the full graph isn't shown, but typically, for direct variation, the line must pass through \((0,0)\). However, since the original problem likely has other graphs (maybe a standard direct variation graph with \( y = kx \) through origin). But based on the given, but since the user's image might have more graphs (like a line through (0,0), a line with slope k through (0,0), etc.). But based on the standard, direct variation graphs are straight lines through the origin. So we need to identify three graphs where the line passes through \((0,0)\). (Note: Since the user's image might have other graphs, but assuming typical options, the correct graphs would be those with lines passing through the origin. For example, if there are graphs like \( y = 2x \) (through (0,0)), \( y = 0.5x \) (through (0,0)), and another linear graph through (0,0). But since the given image has two graphs, maybe the user missed some, but based on the problem statement, we assume the three correct graphs are those with lines passing through the origin (direct variation \( y = kx \) form).

Answer:

(Assuming typical options, the three graphs with lines passing through the origin (0,0). For example, if the options include graphs like:

• A graph with line through (0,0) and (1, k)
• Another with line through (0,0) and (2, 2k)
• Third with line through (0,0) and (3, 3k)

These would be the three options. But since the image is partial, the key is direct variation graphs are straight lines through the origin.)