Is the relationship between the width and length of the patio linear? why or why not

The relationship is not linear.

A linear  relationship can be represented by

y = k*x

Which means that the increments or decrements of x, have a proportional gain that corresponds to the changes of y

In the case of the picture

The length

l = 2*w - 5

has the same appearance as the slope intercept form of the equation of the line. However, the constant -5  adds a negative offset to the graph that dissolves the linearity between the variables l and w.

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step-by-step explanatio89