Question

Is \[8y = x\] a direct variation, inverse variation, joint or neither?

Answer 1

Hint: If there are two quantities then an increase in one quantity results in an increase in another quantity, we call it direct variation. If an increase in one quantity results in a decrease in another quantity, we call it an inverse variation. If an expression is given, we need to give values to any of the variables to find the value of another variable. By observing that we can find whether the given expression is a direct variation or inverse variation.

Complete step by step answer:
The given expression is \[8y = x\]. Here there are two variables x and y.
The given expression can be written as \[x = ky\] where \[k\]is a constant which has a constant value eight.
Now let us find the values of x by giving values to y. We will start with\[1,2,3,...\]
Let y be one, \[y = 1\]
\[x = 8 \times 1 = 8\]
Thus, when \[y = 1\]then\[x = 8\]
Let y be two, \[y = 2\]
\[x = 8 \times 2 = 16\]
Thus, when \[y = 2\]then \[x = 16\]
Let y be three, \[y = 3\]
\[x = 8 \times 3 = 24\]
Thus, when \[y = 3\]then \[x = 24\]
Let y be four, \[y = 4\]
\[x = 8 \times 4 = 32\]
Thus, when \[y = 4\]then \[x = 32\]
From the above calculations, we can observe that when the value of y increases then the value x also increases.
Thus, \[8y = x\] cannot be inverse variation, joint, or neither. \[8y = x\] is a direct variation.

Note: To find the relation between any two variables when any expression is given, we will start assigning values to any one of the variables and check how other variables change, increase, or decrease. Using this we can find whether the variables are in direct variation or inverse variation.