The graph will be a straight line with a slope of 3 and an intercept at the origin (0, 0).
The relationship between the perimeter and side lengths of an equilateral triangle:
Graph represents perimeter: This confirms that the graph depicts the function y = f(x), where y is the perimeter and x is the side length of the triangle.
Equilateral triangle: All three sides of an equilateral triangle have the same length, denoted by x in this case.
Slope of 3: This indicates a linear relationship between x and y with a constant rate of change of 3 units of perimeter for every 1 unit increase in side length.
Y-intercept of 0: This means when the side length is 0 (no triangle), the perimeter is also 0, as expected.
Based on these points, we can conclude that the function representing the perimeter of the equilateral triangle is:
y = 3x
This equation reflects the fact that the perimeter is simply the sum of all three side lengths, which are all equal to x, multiplied by the constant factor of 3.
Therefore, the graph will be a straight line with a slope of 3 and an intercept at the origin (0, 0).