A spring with a 2-pound weight suspended is 9 inches in length. With a 5-pound weight suspended, the length increases to 13.5 inches.
Which equation does not represent the behavior of the spring?
y – 2 = 1.5(x – 9)
y – 9 = 1.5(x – 2)
y = 1.5x + 6
y – 13.5 = 1.5(x – 5)
I looked it up and according to Hook's Law, the relation is linear.
so you have two points (2,9) and (5,13.5)
slope = (13.5-9)/(5-2)
= 1.5
Using (2,9) my equation would be
y-9 = 1.5(x-2)
Using (5,13.5) would produce
y-13.5 = 1.5(x-5)
clearly the second one is wrong
The equation that does not represent the behavior of the spring is:
y – 13.5 = 1.5(x – 5).
To determine which equation represents the behavior of the spring, we can analyze the given information about the weights and lengths.
We are told that when a 2-pound weight is suspended, the length of the spring is 9 inches. Using this information, we can create an equation in point-slope form, which is (y – y1) = m(x – x1), where (x1, y1) represents the coordinates of a point on the line and m represents the slope of the line.
Using the point (9, 2), the equation representing the behavior of the spring is:
y – 2 = m(x – 9)
Similarly, when a 5-pound weight is suspended, the length of the spring increases to 13.5 inches. We can create another equation using the point-slope form.
Using the point (13.5, 5), the equation representing the behavior of the spring is:
y – 5 = m(x – 13.5)
Now, we can compare this equation with the given options:
1. y – 2 = 1.5(x – 9) - This equation is consistent with the information given.
2. y – 9 = 1.5(x – 2) - This equation does not represent the behavior of the spring.
3. y = 1.5x + 6 - This equation does not represent the behavior of the spring.
4. y – 13.5 = 1.5(x – 5) - This equation is consistent with the information given.
Therefore, the equation that does not represent the behavior of the spring is:
y – 9 = 1.5(x – 2)