In chemistry class you might write an equation in that fashion to suggest that 1 molecule of water is composed of the "sum" of 1 oxygen atoms and 2 hydrogen atoms.
In your math work, since you are doing the topic of "direct variation" you are expected to think about how the quantities vary. That means an equation of the form y = kx, where k is a constant and x and y are the variables.
In this case, what is asked for is the ratio of hydrogen to oxygen, which is constant no matter how many molecules you are talking about.
For example, you could have (oxygen, hydrogen) values of (1, 2), (2, 4), (3, 6), (4, 8), etc.
This can be expressed as H = 2O, in other words, number of hydrogen atoms is two times whatever the number of oxygen atoms.
y = k * x
H = 2 * O
In this case, the equation is expressing how hydrogen "varies directly" with oxygen. The constant of variation is 2.
You could also write this:
y = k * x
O = (1/2) * H
That would express how oxygen varies directly with hydrogen. The constant of variation is 1/2.
Graph of y = kx is a line through (0, 0) always. The slope of the line is k.
So instead of an "addition" equation, direct variation is always a "multiplication" equation.
Note: If you have a situation that does not pass through (0, 0), it is not considered "direct variation."
So, y = 3x + 5 is not direct variation.
Thank you very much for explaining it to me. I am taking my first algebra course and I am having a difficult time in undestanding my text. You made this so clear. I really appreciate it. thanks Ann
COrrect ! great job