Question

How can you identify a linear nonproportional relationship from a table, a graph, and an equation?

Answer 1

The graph of a non-proportional linear relationship is a straight line that does not pass through the origin.
Non-proportional linear relationships can be expressed in the form y = m x + b
With increase in proportion of one quantity, the proportion of the other quantity decreases and with decrease in proportion of one quantity , the proportion of the other quantity increases .

Explanation:
From Graph :
The graph of a non-proportional linear relationship is a straight line that does not pass through the origin.
From Equation :
Non-proportional linear relationships can be expressed in the form y = m x + b, where , m is the slope of the line, and b represents the y-intercept.

From Table:
With increase in proportion of one quantity, the proportion of the other quantity decreases and with decrease in proportion of one quantity , the proportion of the other quantity increases .

Answer 2

Explanation:

If b = 0 in a linear equation (so y = mx), then the equation is a proportional linear relationship between y and x.

If b ≠ 0, then y = mx + b is a non-proportional linear relationship between y and x.