When we say that a variable varies directly as another variable, or is directly proportionate to another variable, we mean that the variable changes with the same ratio as the other variable increases.
This kind of correlation can be represented as a linear function that passes through the origin, the equation of which is of the form . The two variables we are considering are <em>x</em> and <em>y</em>, while <em>k</em> is called the constant of proportionality.
We know the constant of proportionality k = -3, applying the above definition we get that the equation is .
Aryana simplified the expression 3(x + 4) + 2(2x – 3). She justified her work by letting x = 3 in both the given and simplified expressions. Which is the correct simplified expression for Aryana's expression? What is the result for both expressions when x = 3?
