Question

screw hooks are used to hang plants and other decorations from walls and ceilings. the graph shows the total mass, in grams, of a can based on the number of screw hooks in the can.

mass of screw hooks in a can

(the graph has a y - axis labeled mass (grams) with values from 0 to 600 and an x - axis labeled number of screw hooks with values from 0 to 30. a line is plotted on the graph.)

which of the following is the interpretation of the y - intercept of this graph?

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a graph \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept) occurs when \(x = 0\). In the context of this problem, \(x\) represents the number of screw hooks, and \(y\) represents the total mass of the can (in grams).

Step2: Interpret \(x = 0\) in the context

When \(x = 0\), it means the number of screw hooks in the can is \(0\). So the y - intercept (the value of \(y\) when \(x = 0\)) represents the mass of the can when there are no screw hooks in it.

(Note: Since the options are not provided, we can only give the general interpretation. If options were provided, we would match this interpretation to the correct option. For example, if an option said "The mass of the empty can (when there are 0 screw hooks)", that would be the correct interpretation of the y - intercept.)

Answer:

The y - intercept represents the mass of the can when the number of screw hooks (\(x\)) is \(0\) (i.e., the mass of the empty can).