Question

How do you write the direct variation equation if $ y=42 $ as $ x=6 $ , find y for the x value 3?

Answer 1

Hint: The direct variation equation can be represented as $ y=kx $ where k is a constant. In the given question we have one y value of an x value. so we can find the value of the constant that is k, when we have the value k we can find the value of y for any x by putting the value of x in the equation.

Complete step by step answer:
We have to write the direct variation equation for $ y=42 $ and $ x=6 $
We know the direct variation equation is $ y=kx $ where k is constant
We can find the value of k= $ \dfrac{y}{x} $ where x is not equal to 0.
The value of k is equal to $ \dfrac{42}{7}=6 $
Now our direct variation equation is $ y=6x $
Now we can find the value of y when x is equal to 3 by replacing x by 3 in the above equation.
So the value of y when x is 3= $ 6\times 3=18 $.

Note:
 Always remember the format of the direct variation equation is $ y=kx $ where k is constant, in this equation the variable y is directly proportional to x. The graph of direct variation equation always passes through the coordinate (0,0) and it is a straight line the slope of the straight line is dependent on the coefficient of proportionality that is k. The value of k van is negative so the slope can be negative.