Question

Suppose y varies directly with x and y=72when x=6 . What direct variation equation relates x and y? What is the value of y when x=10

A. y=1/12x; 120
B. y=12x; 120
C. y=6x; 62
D. y=1/6x; 43.2

Answer 1

In this scenario, you need to understand what it means when y varies directly with x. Since they vary directly, as x increases, so does y. The proportion, also known as factor, stays constant no matter what you plug into x. This is fit by the following equation:
\[y = x\]

In other words, if you plug 5 into x, y should always no matter what be three times larger than x (just an example).

To solve this scenario, you need to find a proportion to use with your y = x formula. You can find the proportion by dividing y=72 by x=6.

\[72/6 = 12\]

Now, to use 12 in the formula. Remember that y is 12 times larger than x when you plug a number for x, so to make y larger, multiply 12 and x.
\[y=12x\]
\[let(x )\rightarrow 6 \]
Plug 6 into x.

Therefore, y = 72 when x = 6.
\[y = 12(6) = 72\]

Answer 2

This is all wrong