Answer the question
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
____ inches
Let's denote "x" as the weight in pounds and "y" as the length of the spring in inches.
We can create a linear equation using the two given points (2, 12) and (5, 18) to find the rate of change (slope) of the spring:
slope = (18 - 12) / (5 - 2)
slope = 6 / 3
slope = 2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - 12 = 2(x - 2)
y - 12 = 2x - 4
y = 2x + 8
To find the length of the spring when no weights are attached (x = 0), we substitute x = 0 into the equation:
y = 2(0) + 8
y = 8
Therefore, the length of the spring when no weights are attached is 8 inches.