Q&A for How to Determine Whether Two Variables Are Directly Proportional

No. A zero slope means there's no change at all; thus, no proportionality at all.

If you're referring to inverse proportionality, such a case can be represented by xy = k, or y = k/x, or x = k/y, where x and y are variables, and k is a constant. If you can express x and y by any of those equations, you know that x and y are inversely proportional to each other (meaning that x goes up at the same rate that y goes down, or vice versa).

It is a "direct variation," because each x value is related identically to the corresponding y value (x = 2y). We call this a direct proportion.

If by linear you mean a straight line on a graph, the answer is yes. The graph of the direct proportion "y = kx" (or y = mx + b) is always a straight line.

It is a variable whose value "depends" on the value of another variable. An example: y = 2x² + 3x + 1. You can't find the value of y until you know the value of x, so y is the dependent variable.

(1) Graph the relationship. If the graph is a straight line having a slope that is neither zero nor infinity, the relationship between the variables is proportional; (2) Inspect the equation to see if it has (or can be made to have) the form y = kx, or x = ky, where k is a constant.

If by linear you mean having a "straight slope," then no.