Use the image to answer the question. %0D%0A%0D%0A%0D%0ADetermine the initial value and the rate of change of the linear function as given in the graph.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AThe initial value is 16, and the rate of change is 32.%0D%0AThe initial value is Start Fraction 1 over 6 End Fraction , and the rate of change is Start Fraction 3 over 2 End Fraction .%0D%0A%0D%0AThe initial value is −23, and the rate of change is 23.%0D%0AThe initial value is negative Start Fraction 2 over 3 End Fraction , and the rate of change is Start Fraction 2 over 3 End Fraction .%0D%0A%0D%0AThe initial value is 23, and the rate of change is −23.%0D%0AThe initial value is Start Fraction 2 over 3 End Fraction , and the rate of change is negative Start Fraction 2 over 3 End Fraction .%0D%0A%0D%0AThe initial value is −2, and the rate of change is 23.
Based on the given graph, it is evident that the line intersects the y-axis at the point (0, 16). Therefore, the initial value of the linear function is 16.
Moreover, as we move 1 unit to the right on the x-axis, the y-coordinate increases by 32 units. Hence, the rate of change, or slope, of the linear function is 32.
Therefore, the correct response is:
The initial value is 16, and the rate of change is 32.