the number of people that can be seated in a lecture hall varies directly with the number of rows of seats. if 72 people can be seated in 4 rows, write a direct variation equation to describe the number of people y that can be seated in x rows. then graph
people (y) = k rows (x)
y = kx
72 = k(4)
k = 18
then y = 18x
To write a direct variation equation, we need to determine the constant of variation. In this case, the constant of variation represents the number of people that can be seated in one row.
Given that 72 people can be seated in 4 rows, we can determine that 72/4 = 18 people can be seated in one row.
Let's denote the number of people as y and the number of rows as x. Based on the given information, we can write the direct variation equation as:
y = kx
where k is the constant of variation.
In this case, we already found that there are 18 people in one row, so the equation becomes:
y = 18x
Now let's graph this equation. The y-axis represents the number of people, and the x-axis represents the number of rows.
To graph it, choose some values for the number of rows, substitute them into the equation to find the corresponding values for people, and plot the points accordingly. Let's choose x = 1, 2, 3, 4, 5 as examples:
For x = 1,
y = 18(1) = 18
For x = 2,
y = 18(2) = 36
For x = 3,
y = 18(3) = 54
For x = 4,
y = 18(4) = 72
For x = 5,
y = 18(5) = 90
Plotting these points on the graph, we get a straight line that passes through the origin and has a positive slope of 18:
```
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90| .
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80|
|
70| .
|
60|
|
50| .
|
40|
|
30| .
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20|
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10| .
|_________________________
0 1 2 3 4
```
This graph represents the direct variation relationship between the number of people and the number of rows in the lecture hall.