Create a table of values from the graph. Then find the value of y when x=20. Use pencil and paper. Find three more pairs of values. Then write a situation you could model using this graph
Complete the table
x 2 _ _ 6
y _ 3.5 4.25 _
x 2 4 6 20
y _ 3.5 4.25 _
To find the value of y when x = 20, we need to gather more data from the graph:
x 2 4 6 20
y _ 3.5 4.25 _
Looking at the pattern, the y-values are increasing by a constant amount each time.
Let's fill in the missing values:
x 2 4 6 20
y 3.5 4.25 5 8.75
Now, let's find three more pairs of values:
x 2 4 6 20
y 3.5 4.25 5 8.75
y 2.75 3 3.5 4.5
y 9 9.5 10 14
A situation that could be modeled using this graph is the following:
An ice cream shop charges a base price for each scoop of ice cream ($2 for the first scoop), and an additional $0.75 for each extra scoop. The x-values represent the number of scoops of ice cream, and the y-values represent the cost in dollars. The graph shows the cost of different numbers of scoops of ice cream. The x-value of 20 represents a situation where a customer purchases 20 scoops of ice cream, and the corresponding y-value of 8.75 represents the cost in dollars for those 20 scoops.
To complete the table of values from the given graph, we already have two values: x=2 and y=3.5. Let's find the remaining values based on the graph.
Using the given graph:
x = 2, y = 3.5
x = 4, y = __
x = 6, y = 4.25
We need to find the missing values. Based on the graph, it seems like the values are increasing linearly, so we can calculate the missing values using a linear equation.
First, find the slope (m) of the line:
m = (change in y) / (change in x) = (4.25 - 3.5) / (6 - 2) = 0.75 / 4 = 0.1875
Now, we can use the slope and one point (2, 3.5) to find the equation of the line:
y = mx + b
3.5 = 0.1875(2) + b
3.5 = 0.375 + b
b = 3.5 - 0.375
b = 3.125
Now that we have the equation of the line, we can find the missing values.
x = 4:
y = 0.1875(4) + 3.125
y = 0.75 + 3.125
y = 3.875
x = 6:
y = 0.1875(6) + 3.125
y = 1.125 + 3.125
y = 4.25
Now that we have completed the table of values, it looks like this:
x 2 4 6
y 3.5 3.875 4.25
To find the value of y when x=20, we can use the equation of the line:
y = 0.1875(20) + 3.125
y = 3.75 + 3.125
y = 6.875
Three more pairs of values could be:
x = 8, y = 4.625
x = 10, y = 5
x = 12, y = 5.375
A situation that could be modeled using this graph is the number of hours studying (x) and the corresponding test scores (y). As the number of hours spent studying increases, the test scores also increase, possibly indicating a positive correlation between studying time and test performance. The graph represents the overall trend, and the table of values provides specific data points.
To create a table of values from the graph, we need to take note of the corresponding y-values for each given x-value.
Looking at the provided x-values, we have 2, _, _, and 6. We also have the corresponding y-values _, 3.5, 4.25, and _.
To find the missing y-values, we need to observe the pattern from the given values. From the given values, we can see that as the x-value increases by 2, the y-value increases by 0.75. So, we can fill in the missing values as follows:
x 2 4 6
y 3.5 4.25 5
Now, let's find the value of y when x=20. Since we don't have a direct value to get the answer from the table, we can use the given pattern to estimate the missing value.
From the pattern observed earlier, we know that as x increases by 2, y increases by 0.75. Therefore, for every increase of 2 in x, there is an increase of 0.75 in y.
To find the value of y when x=20, we need to calculate how many times we have a 2-unit increase from x=6 to x=20.
(20 - 6) / 2 = 14 / 2 = 7
So, for every increase of 2 in x, y increases by 0.75. Since we have a total increase of 7 times, we multiply the increase (0.75) by 7:
0.75 * 7 = 5.25
Therefore, when x=20, y is estimated to be 5.25.
To find three more pairs of values, we can use the pattern observed previously.
Starting from the last given x-value, 6, we can add 2 to get the next value:
x 2 4 6 8 10 12
y 3.5 4.25 5 5.75 6.5 7.25
Now, we have three additional pairs of values: (8, 5.75), (10, 6.5), and (12, 7.25).
To write a situation that could be modeled using this graph, consider a scenario where x represents the amount of time spent studying for a test (in hours) and y represents the corresponding test scores. This graph could represent the relationship between the amount of time a student spends studying and their test scores. The positive slope indicates that as the time spent studying increases, the test scores also increase.