Challenge 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
enter your response here
enter your response here
2.75
enter your response here
4.25
6
enter your response here
To complete the table, we need to find the y-values that correspond to certain x-values using the points provided by the graph. The graph has given us a set of points that allow us to estimate the y-values for particular x-values.
The pattern in the points suggests that as x increases by 1 unit, y increases by 0.75 units, starting from an initial value of y = 0.5 when x = 0. The formula deriving from this pattern could be approximated as:
\[ y = 0.75x + 0.5 \]
Given that, we can complete the table for the missing values:
For x = 2, from the graph we can see that y = 2 (as given in the description).
For the next missing y-value, we don’t have the corresponding x-value, though you’ve indicated an entry next to "2.75" under the y column but not under the x column. So, we'll have to assume an x-value or skip this one. Assuming the sequence continues without skipping any x-values, then the x-value prior to 5 (where y was given as 4.25) would logically be 4. If this is correct, then the y-value when x = 4 would be 3.5 (as given in the description).
For x = 5, we already have the y-value: y = 4.25.
For x = 6, if we apply our formula, y = 0.75(6) + 0.5 = 4.5 + 0.5 = 5. Again, this matches the given point in the description (6, 5).
Now, let's estimate the value of y when x = 20 using the same relationship:
\[ y = 0.75(20) + 0.5 = 15 + 0.5 = 15.5 \]
Your complete table may look something like this:
```
x | y
----------
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
... | ...
20 | 15.5
```
Three more pairs of values (using the formula):
```
x | y
----------
11 | 8.75 (0.75 * 11 + 0.5)
12 | 9.5 (0.75 * 12 + 0.5)
13 | 10.25 (0.75 * 13 + 0.5)
```
A situation you could model using this graph may be the cost of a subscription service where there is a base cost of 50 cents and every hour of service adds an additional 75 cents to the cost. With x representing the hours of service used and y representing the total cost in dollars.