Question: The graph shows the cost of apples at a local market. Use the graph to answer the problems.
Cost ($)
y
x
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 1 2 3 4 5 6 7 8 9 10
Number of Apples
Graph: a scatter plot on a coordinate grid in the top-left, with points lying on a straight line through the origin and increasing by about (1, 0.75) each step; the plotted points appear at approximately (0,0), (1,0.75), (2,1.5), (3,2.25), (4,3), (5,3.75), and (6,4.5), so the line shows direct proportionality with constant of proportionality about 0.75. top-left
2. Find the constant of proportionality. K=
k = .75
1. **State the problem:** We need to find the constant of proportionality $k$ from the graph showing the cost of apples versus the number of apples.
2. **Understand the relationship:** The graph shows a straight line through the origin, indicating a direct proportionality between cost $y$ and number of apples $x$. The formula for direct proportionality is:
$$y = kx$$
where $k$ is the constant of proportionality.
3. **Identify points from the graph:** From the graph, some points are approximately:
- $(0,0)$
- $(1,0.75)$
- $(2,1.5)$
- $(3,2.25)$
4. **Calculate $k$ using a point:** Using the point $(1,0.75)$,
$$k = \frac{y}{x} = \frac{0.75}{1} = 0.75$$
5. **Verify with another point:** Using $(2,1.5)$,
$$k = \frac{1.5}{2} = 0.75$$
This confirms the constant of proportionality is consistent.
6. **Final answer:**
$$\boxed{k = 0.75}$$