The graphs of three functions are shown.[img]https://cdn.openupresources.org/uploads/pictures/8/8.5.B4.2.23.new.png[/img][list=1][*]Match one of these equations to each of the graphs.[list=1][*]d=60t, where d is the distance in miles that you would travel in thours if you drove at 60 miles per hour.[/*][*]q=50−0.4d, where q is the number of quarters, and d is the number of dimes, in a pile of coins worth $12.50.[/*][*]A=πr2, where A is the area in square centimeters of a circle with radius r centimeters.[/*][/list][/*][*]Label each of the axes with the independent and dependent variables and the quantities they represent.[/*][*]For each function: What is the output when the input is 1? What does this tell you about the situation? Label the corresponding point on the graph.[/*][*]Find two more input-output pairs. What do they tell you about the situation? Label the corresponding points on the graph.[/*][/list]
Student Response[list=1][*][list=1][*]B. This graph represents a proportional relationship with a constant positive slope. [/*][*]C. This is the only one of the graphs, and the only equation, with a negative slope and vertical intercept of 50.[/*][*]In figure A, we have point (1,π), representing the fact that a circle of radius 1 cm has area π cm2.[br]In figure B, we have point (1,60), representing the fact that after traveling for 1 hour at 60 miles per hour, you would travel 60 miles.[br]In figure C, we have point (1,49.6). This does not have a concrete interpretation in terms of the context, as it says that if you had only one dime, you would have 49.6 quarters.[br]See answer to part 4 for the graphs.[/*][*]In figure A, we mark the points (2,4π) and (3,9π), representing the fact that circles of radius 2 cm and 3 cm have respective areas 4π cm2 and 9πcm2.[br]In figure B, we mark the points (2,120) and (3,180), representing the fact that after traveling for 2 and 3 hours at 60 miles per per hour, you would respectively travel 120 and 180 miles.[br]In figure C, we mark the points (40,34) and (80,18), representing the fact that if there were 40 or 80 dimes in the pile, there would have to be 34 and 18 quarters, respectively.[img]https://cdn.openupresources.org/uploads/pictures/8/8.5.B4.2.23sol.new.png[/img][/*][/list][/*][/list]