Question

which of the following is the interpretation of the y - intercept of this graph?
a. the mass of the can only
b. the mass of 1 screw hook
c. the mass of 10 screw hooks
d. the mass of the can and x screw hooks

Explanation:

To determine the interpretation of the y - intercept, we recall that in a linear relationship \(y = mx + b\), the y - intercept (\(b\)) occurs when \(x = 0\). In the context of this graph, the x - axis represents the number of screw hooks. When \(x = 0\) (i.e., there are 0 screw hooks), the y - value represents the mass of the can only (since there are no screw hooks added to the can).

• Option A: When \(x = 0\) (number of screw hooks is 0), the y - intercept gives the mass of the can only. This is consistent with the definition of a y - intercept in a context where \(x\) is the number of screw hooks.
• Option B: The mass of 1 screw hook would be related to the slope (the rate of change of mass with respect to the number of screw hooks), not the y - intercept.
• Option C: The mass of 10 screw hooks would be a value on the line when \(x = 10\), not the y - intercept (which is at \(x = 0\)).
• Option D: The mass of the can and \(x\) screw hooks is given by the equation \(y=\text{mass of can}+\text{mass per screw hook}\times x\), and when \(x = 0\), it's just the mass of the can, not the can and \(x\) screw hooks (since \(x = 0\) here).

Answer:

A. the mass of the can only