Answer:
rate of change = 15 (answer D)
Step-by-step explanation:
Notice that the graph that represents the relationship is a straight line. They also give you specific points on the plane that one can use for finding the answer to the requested rate of change.
The actual rate of change is the quotient of how much the function "rises" vertically for a given horizontal "run."
Rate of Change = [tex]\frac{rise}{run}[/tex]
In the attached image I have depicted in red the "rise" of the graph from one of the given points to the next. In green you see depicted what the associated horizontal "run" is.
Notice that the vertical "rise" is from a y-value of 30 to a y-value of 45, giving a net of 15 units of "change".
Notice also, that such rise corresponds to a horizontal change from the value 2 to the value 3, This represents a "run" or horizontal change of one (1) unit.
Finally, we can then write the rate of change for this relationship to be:
Rate of Change = [tex]\frac{rise}{run}=\frac{15}{1}=15[/tex]
