Suppose that a city operates two neighborhood schools, one in the rich neighborhood and one in the poor neighborhood. The schools are equal in size and currently have equal budgets. The city receives $10 million in federal grant money that can be used to supplement the budgets of the two schools, which are initially identical. For each school, the average score on a standardized achievement test depends on how many dollars are allocated to the school. Letting S denote the average test score and X denote additional spending in millions of dollars, the relationships between scores and additional spending for the two schools are as follows: Spoor = 40 + Xpoor, Srich = 45 + 3Xrich.

Required:
a. Plot the above relationships and interpret the differences between the slopes and intercepts in intuitive terms.
b. Derive and plot the community’s transformation curve between Srich and Spoor, remembering that Xpoor and Xrich must sum to 10. Because of the linear relationship between S and X for each group, the transfor- mation curve is a straight line.
c. Find and plot the test scores that would result if the city divided the grant money equally between the schools.
d. Find and plot the test scores that would result if the city allocated the grant money to equalize the scores across schools.