Question

The variables x and y vary directly, and y=10 when x=2. Write an equation that relates x and y. What is the result when x=9?

y= ?

Answer 1

The equation relating variables x and y in direct variation is y = 5x. To find y when x = 9, we substitute 9 into the equation to find that y equals 45.

Step-by-step explanation:

When variables x and y vary directly, it means that as x increases, y increases at a constant rate, and this relationship can be represented by the equation y = kx, where k is the constant of proportionality. Given that y=10 when x=2, we can find k by substituting these values into the equation:

10 = k × 2

k = 5

Now we can write the direct variation equation as y = 5x. To find the value of y when x=9, we simply substitute 9 into the equation:

y = 5 × 9

y = 45

Therefore, when x = 9, the value of y is 45.