The direct variation equation relating x and y is y = 10x.
What is the meaning of direct variation?
Direct variation between two quantities implies that an increase in one increases the other, and a decrease in one decreases the other.
Its shown as a ∝ b, where a and b are the two quantities and ∝ is the sign of proportionality or variation. To remove the sign and put an equal sign, we have to put in a constant of proportionality like this, a = kb, where k is the constant of proportionality.
How to solve the question?
In the question, we are informed that y varies directly with x.
This can be shown as y ∝ x, as discussed above.
To remove the sign of proportionality, we add in a constant of proportion as follows: y = kx.
Now, we are informed that y = 30 when x = 3.
Substituting these values in the equation, we get:
y = kx,
or, 30 = k*3, {Substituting}
or, 3k = 30, {Rearranging}
or, 3k/3 = 30/3, {Dividing the equation by 3}
or, k = 10 {Simplifying}.
Substituting k = 10 in the original equation, we get:
y = kx,
or, y = 10x {Substituting}.
Thus, the direct variation equation relating x and y is y = 10x.
Learn more about direct variation at
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