hallenge Create a table of values from the graph. Then find the value of y when xequals
20.
Use pencil and paper. Find three more pairs of values. Then write a situation you could model using this graph.
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Part 1
012345678910
012345678910xy
A horizontal x-axis is labeled from 0 to 10. A vertical y-axis is labeled from 0 to 10. A line rises from left to right and passes through the following points: (0, 0.5); (1, 1.25); (2, 2); (3, 2.75); (4, 3.5); (5, 4.25); (6, 5); (7, 5.75); (8, 6.5); (9, 7.25); (10, 8).
...
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Part 1
Complete the table.
x
y
2
2
3
2.75
5
4.25
6
5
Part 2
When xequals
20,
the value of y is 75
.
To complete the table using the points provided by the graph, we need to see if there's an observable pattern or relationship that we can use for finding the y-value when x = 20. Let's start by listing the given points.
\[
\begin{array}{c|c}
x & y \\
\hline
0 & 0.5 \\
1 & 1.25 \\
2 & 2 \\
3 & 2.75 \\
4 & 3.5 \\
5 & 4.25 \\
6 & 5 \\
7 & 5.75 \\
8 & 6.5 \\
9 & 7.25 \\
10 & 8 \\
\end{array}
\]
From these points, we can observe that as x increases by 1, y increases by 0.75 (i.e., 1.25 - 0.5 = 0.75, 2 - 1.25 = 0.75, etc.). This suggests a linear relationship where the slope (or rate of change) is 0.75. We can use this to find more pairs of values and to extrapolate the value of y when x equals 20.
However, it's worth noting that there is a stated inconsistency in the question, as the textual representation provided for when x equals 20 is 75, which would not be possible if we were to follow the linear pattern mentioned above. The linear pattern would suggest that y should equal 15.5 when x is 20 (since 0.75*20 + 0.5 = 15.5). There seems to be a discrepancy here.
Nonetheless, following the pattern of the points, I'll provide a few more pairs based on extrapolating the y-values based on x:
\[
\begin{array}{c|c}
x & y \\
\hline
11 & 8.75 \\
12 & 9.5 \\
13 & 10.25 \\
14 & 11.0 \\
\end{array}
\]
Now, let's write a situation that could be modeled using this graph. Since this is a linear relationship, we could be looking at something like a simple savings model, where x represents time in weeks and y represents the amount of money saved in hundreds of dollars.
**Situation Example:**
Alice is saving money for a new bicycle. Every week, she saves an extra $75, on top of an initial $50 saved during her first week. The graph shows her progress over a 10-week period.
In this situation, Alice starts with $50 in her savings, which correlates to the y-value when x (time in weeks) equals 0. For every week that passes, she adds $75 to her savings. After 10 weeks, she has saved $800, consistent with the graph. The table helps to illustrate her savings at various points in time.