Homework Clinic
Social Science Clinic => Economics => Topic started by: xsk4r3kr0w on Nov 23, 2022
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Slope of a Curve at a Point
The table shows the relationship between X and Y.
| Point | X | Y |
| A | 1 | 79 |
| B | 2 | 49 |
| C | 3 | 39 |
| D | 4 | 34 |
| E | 5 | 31 |
| F | 6 | 29 |
What is the slope across the arc between points A and B? What is the slope across the arc between points E and F?
◦ 30, 2
◦ 2, 30
◦ -30, -2
◦ -2, -30
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-30, -2
The slope of the arc between points A and B is the change in Y (between A and B) divided by the change in X (between A and B).
The change in Y can be calculated as Y at point B (49) minus Y at point A (79) = -30
The change in X can be calculated as X at point B (2) minus X at point A (1) = 1
Therefore, the slope of the arc between A and B = -30/1 = -30
The slope of the arc between points E and F is the change in Y (between E and F) divided by the change in X (between E and F).
The change in Y can be calculated as Y at point F (29) minus Y at point E (31) = -2
The change in X can be calculated as X at point F (6) minus X at point E (5) = 1
Therefore, the slope of the arc between E and F = -2/1 = -2