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(12.) The population of Michigan is nearly 10,000,000 people as Massachusetts has nearly 6,000,000

people. The number of state representatives is 15 and 10, respectively.
a. Write the equation of the line given the state population and appointed state representatives.
b. What does the slope represent?
c. What does the y-intercept represent?
d. Use your model to predict how many state representatives that the state of New York will be
assigned if they have a population of 19,000,000.

User Neskews
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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
User Ashok Dey
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