The graph and the evaluation between the quantities, number of people and hours worked are presented as follows;
First question; Please find attached the graph of the ordered pairs obtained from the table showing the number of people picking strawberries from a field and the corresponding number of hours they worked, created with MS Excel
Second question; The line in the graph does not pass through the origin, therefore, the graph does not represent two quantities that are proportional to each other
The steps used to obtain the graph is as follows;
First question
The values in the table can be presented as ordered pairs indicating the location of (x, y) points on the graph as follows;
(1, 3), (7, 1), and (4, 2)
The above points can be arranged in increasing x-values, to get; (1, 3), (4, 2), and (7, 1), which shows a constant negative first difference indicating a linear graph with a negative slope of 1
The above points can be entered into adjacent cells in MS Excel, in the same form that they appear in the table, select all the entered data then use the Insert then Charts Menu function in MS Excel to create a scatter plot for the data
Second question
The equation of the best fit line in the graph representing the relationship between the two quantities can be found as follows;
Slope of the line is; (2 - 3)/(4 - 1) = -1/3
Equation of the line in point and slope form is therefore;
y - 3 = (-1/3) × (x - 1)
y = -x/3 + 1/3 + 3
y = 10/3 - x/3
The y-intercept of the above equation is 10/3, which indicates that the graph does not pass through the origin, therefore, the relationship between the two quantities is not a proportional relationship