If there is an increase in a series at constant rate, the graph will be a _______.
${\text{A)}}$ Convex curve
${\text{B)}}$ Concave curve
${\text{C)}}$ A straight line from left top to right bottom
${\text{D)}}$ A straight line from left bottom to right top
Answer
640.2k+ views
Hint: To find the answer without any doubt, we have to assume and consider a series first, and then increase the series at a constant rate i.e., with the same amount or number.
After that, we will represent in a graph and also we will be able to see the cures and lines clearly
Finally we get the required answer.
Complete step-by-step solution:
Let us assume a simple series distribution which is increasing at constant rate:
Here, every number is increasing by $5$ (thus at constant rate)
Now, representing this table in the graph, we get:
As we can see, the change in the graph is a straight line from left bottom to right top.
Hence we can conclude the correct option is (D) A straight line from left bottom to right top.
Note: In this question we have an alternative logical answer as follows:
Basically a series consists of a sequence with some common operations in it and almost in every case, the number will be increasing in certain rate and sometimes it will be in a decreasing rate too.
Considering in that way, when the numbers are increasing at a constant rate, the difference between the points will be the same and the points in the graph will also increase in a constant rate as the difference is the same, thus we will get a straight line from left bottom to right top.
In case, if the series is decreasing at a constant rate, the graph will be a straight line from left top to right bottom.
After that, we will represent in a graph and also we will be able to see the cures and lines clearly
Finally we get the required answer.
Complete step-by-step solution:
Let us assume a simple series distribution which is increasing at constant rate:
| ${\text{x}}$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
| ${\text{y}}$ | $5$ | $10$ | $15$ | $20$ | $25$ | $30$ |
Here, every number is increasing by $5$ (thus at constant rate)
Now, representing this table in the graph, we get:
As we can see, the change in the graph is a straight line from left bottom to right top.
Hence we can conclude the correct option is (D) A straight line from left bottom to right top.
Note: In this question we have an alternative logical answer as follows:
Basically a series consists of a sequence with some common operations in it and almost in every case, the number will be increasing in certain rate and sometimes it will be in a decreasing rate too.
Considering in that way, when the numbers are increasing at a constant rate, the difference between the points will be the same and the points in the graph will also increase in a constant rate as the difference is the same, thus we will get a straight line from left bottom to right top.
In case, if the series is decreasing at a constant rate, the graph will be a straight line from left top to right bottom.
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