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Answer:
a. Please find attached the plot of the points (0, 0) and (5, 15)
b. The point (0, 0) represents the start point
The point (5, 15) represents the point in the relationship between the water level and the change in time after 5 seconds
c. Please find attached the graph showing the Linear Trendline drawn between the points (0, 0) and (5, 15)
d. The line represents the possible combination time and water level during filling the bucket
e. The equation of the line is y = 3·x
Step-by-step explanation:
The rate at which the empty bucket is filled = 3 inches per second
a. Please find attached the plot made with Microsoft Excel of the points (0, 0) and (5, 15)
b. The points in part (a) (0, 0) and (5, 15) represent the following stages;
1) The point (0, 0) represents the point where the bucket is initially empty before filling the bucket with water
2) The point (5, 15) represents the 5 seconds of filling the bucket with water to a level of 15 inches
c) Please find attached the plot of the points with a Linear Trendline drawn between the points created with Microsoft Excel
d. The straight line drawn from point (5, 15) and passing through the origin at (0, 0) represents the proportional relationship between the water level in the bucket and the amount of time used in filling the bucket
e. The equation of the line is the equation of a proportional relationship which can be expressed in the following form;
y = kx
k = y/x
At the point (5, 15), we have;
y = 15, and x = 5
∴ k = 15/5 = 3 = The rate at which the bucket is filled with water
k = 3
Therefore, we have;
y/x = k = 3
∴ y/x = 3
y = 3 × x = 3·x
The equation of the line is therefore;
y = 3·x
