We know that the sum S of the exterior angle measures of a polygon with n sides is 360°. This gives us the following equation.
S=360
We want to find four points that satisfy the equation. Then, we want to determine if the equation is linear. In our equation, the value of S is 360 for all possible values of n. This means that we can chose any number of sides of the polygon. Let's chose polygons with 3, 4, 5, and 6 sides. We will write the points in a table of values.
Sidesn
SumS
Point(n,S)
3
360
( 3, 360)
4
360
( 4, 360)
5
360
( 5, 360)
6
360
( 6, 360)
Now, we can plot the points (3,360), (4,360), (5,360), and (6,360) in a coordinate plane.
Next, we want to find out if the equation is a linear equation. The graph of a linear equation is a line. We see that it is possible to draw a horizontal line through all of our points. Let's do it!
This means that the equation is a linear equation.
Extra
Horizontal Lines
All horizontal lines are linear equations with a slope m of 0. Let's see what this looks like in slope-intercept form.
y= mx+ b ⇒ y= 0x+ b
This means that the equation of any horizontal line reduces to be y= b, where b is the y-intercept. In our case, the y-intercept is 360.
y= b ⇒ y= 360
Let's consider the given equation once again.
S=360
We want to know if n=2 is a value that makes sense in the given context. The point (2,360) does satisfy the equation. However, n=2 means that the polygon has two sides. We know that it is not possible to create a polygon with only two sides because polygons must enclose a space.
Therefore, the value n=2 does not make sense in the context of the problem.
