Final answer:
The relationship between the number of stuffed animals and the number of action figures is directly proportional; graphing the given points (20, 15) and (60, 45) results in a straight line with the equation y = (3/4)x, which passes through the origin, confirming the proportionality.
Step-by-step explanation:
The linear relationship between the number of stuffed animals (x) and the number of action figures (y) can be represented on a graph. Given two points, (20, 15) and (60, 45), we can plot these on a Cartesian plane with stuffed animals on the x-axis and action figures on the y-axis. To determine if the relationship is proportional, we look for a straight line that passes through the origin (0,0).
First, let's find the slope (m) of the line by using the formula m = (y2 - y1) / (x2 - x1). Using our points, m = (45 - 15) / (60 - 20) = 30 / 40 = 3 / 4. The equation of the line can be written as y = mx + b, where b is the y-intercept. To find b, we can use one of our points and substitute the values for x, y, and m into the equation y = mx + b and solve for b.
Using the point (20, 15): 15 = (3/4)(20) + b, which simplifies to 15 = 15 + b, indicating that b = 0. Therefore, the equation of the line is y = (3/4)x, and the graph of this equation will be a straight line that passes through the origin, showing a directly proportional relationship between x and y.