Question

the relationship between the perimeter and side length of a regular octagon is shown in the graph below

what happens to the perimeter of a regular octagon as its side length increases by 1?

the perimeter increases by 18
the perimeter increases by 1
the perimeter increases by 4
the perimeter increases by 8

Explanation:

Step1: Recall Octagon Perimeter Formula

A regular octagon has 8 equal sides. The perimeter \( P \) of a regular octagon with side length \( s \) is given by \( P = 8s \). This is a linear relationship, so the graph should be a straight line with slope 8.

Step2: Analyze Slope Interpretation

The slope of the line (change in perimeter over change in side length) represents how much the perimeter changes when the side length changes by 1. From the formula \( P = 8s \), the slope is 8. So when \( s \) increases by 1, \( P \) increases by \( 8\times1 = 8 \). We can also check the graph: for example, when \( s = 1 \), \( P = 8 \); when \( s = 2 \), \( P = 16 \). The change in \( P \) is \( 16 - 8 = 8 \) when \( s \) increases by 1.

Answer:

The perimeter increases by 8 (the option corresponding to "The perimeter increases by 8").