To find the length of the spring when no weights are attached, let's use the rate of change formula:
rate of change = (change in y) / (change in x)
In this case, the "y" value represents the length of the spring and the "x" value represents the weight attached.
Let's take two points on the graph:
Point 1: (2 pounds, 12 inches)
Point 2: (5 pounds, 18 inches)
Using the rate of change formula, we can calculate the change in length of the spring when the weight is increased from 2 pounds to 5 pounds:
rate of change = (18 - 12) / (5 - 2)
= 6 / 3
= 2 inches/pound
This means that for every additional pound of weight, the spring length increases by 2 inches.
To find the length of the spring when no weights are attached (0 pounds), we can use the point-slope formula:
y - y1 = m(x - x1)
Using Point 1 (2 pounds, 12 inches):
y - 12 = 2(0 - 2)
y - 12 = -4
y = 8
Therefore, the length of the spring when no weights are attached is 8 inches.
A spring has a length of 12 inches when a 2-pound weight is attached, and a length of 18 inches when a 5-pound weight is attached. Use rate of change to find the length of the spring when no weights are attached. (1 point) y2-y1/x2-x1
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