Use the graph to answer the questions.

Question

10, 50, 7, 35, 3, 15, 2, 10, 1, 5

a. The constant of proportionality is ______________
b. Write an equation that represents the linear graph. _______________
c. This is a proportional relationship because the graph shows ______________
Options: 2y = x, y = 5x, a constant rate of change, a linear relationship, 2, the points are connected, 5, linear with a y-intercept at (0, 0), 1/2, 1, 1/2y = x, 5y = x, 1/5

Answer 1

To answer your questions, we need to analyze the given data points.

Given pairs:

• (1, 5)
• (2, 10)
• (3, 15)
• (7, 35)
• (10, 50)

a. The constant of proportionality (k) is the ratio of y to x. For example:

• For (1, 5): k = 5/1 = 5
• For (2, 10): k = 10/2 = 5
• For (3, 15): k = 15/3 = 5
• For (7, 35): k = 35/7 = 5
• For (10, 50): k = 50/10 = 5

Thus, the constant of proportionality is 5.

b. The equation that represents the linear graph can be written using the formula y = kx, where k is the constant of proportionality found earlier. Here, k = 5. Therefore:

The equation is: y = 5x.

c. This is a proportional relationship because the graph shows a constant rate of change, which can also be described as linear with a y-intercept at (0, 0) and all points lie along a straight line that passes through the origin.

So, the completed statements will be:

a. The constant of proportionality is 5.
b. Write an equation that represents the linear graph: y = 5x.
c. This is a proportional relationship because the graph shows a constant rate of change (or you could also say linear with a y-intercept at (0, 0)).