a. The equation of the line can be found using two points, (10,000,000, 15) and (6,000,000, 10). The slope of the line can be found using the formula (y2-y1)/(x2-x1). The y-intercept can be found using one of the points and the slope. So, the equation of the line is:
y = mx + b
where m is the slope and b is the y-intercept.
m = (15 - 10) / (10,000,000 - 6,000,000) = 0.005
b = 15 - (0.005 * 10,000,000) = -5,000
y = 0.005x - 5,000
b. The slope of the line represents the change in the number of state representatives for a given change in the state population. In this case, the slope of 0.005 means that for every 1,000,000 people in the population, the number of state representatives increases by 0.005 * 1,000,000 = 5.
c. The y-intercept of the line represents the number of state representatives that the state would have if the population was 0. In this case, the y-intercept of -5,000 means that if the population was 0, the state would have -5,000 state representatives, which is not possible.
d. To predict the number of state representatives for a population of 19,000,000 in New York, substitute 19,000,000 for x in the equation of the line:
y = 0.005x - 5,000
y = 0.005 * 19,000,000 - 5,000 = 95,000 - 5,000 = 90,000
So, the model predicts that New York would have 90,000 state representatives if they have a population of 19,000,000