Question

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How can you identify a linear nonproportional relationship from a table, a graph, and an equation?
From a table, for an ordered pair (0, y), y will not be_____. From a graph, the y−intercept will not be_____. From an equation, it will have the form y = mx + b where b is not ____.

Answer 1

Answer: The number 0 goes in all three blanks.

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Explanation:

A linear proportional relationship always has a y intercept of 0. Visually, this means the proportional graph will go through the origin. So that in turn means b = 0.

For example, the equation y = 5x is a proportional equation with 5 being the constant of proportion. Whatever x is, multiply by 5 to get y. We can think of y = 5x as y = 5x+0 to see that b = 0 here.

When considering nonproportional equations, we let b equal anything but zero. In other words, b is nonzero in this case. Something like y = 5x+2 is not proportional. The graph doesn't go through the origin and the intercept here is (0,2).

In short, you'll write "0" without quotes into each blank.