The perimeter of a square is four times the length of one side. What is the graph of this relationship?
My choices are:
A. A line with a negative slope
B. A horizontal line
C. A vertical line
D. A line with a positive slope
To understand the relationship between the perimeter of a square and the length of one side, we need to use some algebraic expressions.
Let's say that the length of one side of the square is represented by the variable "s". The perimeter of a square is found by adding up the lengths of all four sides, so it can be expressed as 4s.
According to the given information, the perimeter of the square is four times the length of one side. Mathematically, this can be written as:
Perimeter = 4s
Now, to graph this relationship, we need to plot the values of the perimeter and the length of one side on a coordinate plane.
Using any pair of values, we can calculate the perimeter and plot the points. For simplicity, let's choose two values:
When s = 1, the perimeter = 4 * 1 = 4
When s = 2, the perimeter = 4 * 2 = 8
So, we have two points: (1, 4) and (2, 8).
Plotting these points on a graph, we can connect them with a straight line. Since the relationship is linear (directly proportional), the graph will be a straight line passing through the origin (0,0).
Thus, the graph of this relationship would be a straight line with a positive slope passing through the points (1, 4) and (2, 8).