Question

In 2000, the minimum wage in Washington was $6.50 per hour. In 2010, it was $8.55 per hour.

(a) If x is the number of years past 2000 (so in 2000, and in 2010, ), and y is the minimum wage per hour, write two ordered pairs representing the minimum wages given.


(b) What is the slope of the line between these two points? What does the slope specifically represent here?



(c) What is the y-intercept? What does the y-intercept specifically represent here?


(d) Find the equation of this line – write your final answer in slope-intercept form.




(e) Write your equation as a function of x.


(f) If you do not earn a college degree and you are earning minimum wage in 2020, what do you predict you will be earning per hour?




1. In 2002, the greatest number of movie tickets in a single year were sold in America, at 1.58 billion. This is down to 1.27 billion (annualized) for 2010.

(a) Write the linear equation modeled by these two points in slope-intercept form (let in 2000).


(b) Interpret the slope specifically in real world terms. What reasons could you give for this trend?



(c) Interpret the y-intercept specifically in real world terms, and why is this not true given the original description of the data? (If you didn’t use in 2000, your answer here will be wrong.)

Answer 1

a.) Two ordered pairs are (0, 6.50) and (10, 8.55)

b.) slope = (y2 - y1)/(x2 - x1) = (8.55 - 6.50)/(10 - 0) = 2.05/10 = 0.205
The slope represents the amount with which the minimum wage increased per year.

c.) y-intercept is the value of y when x = 0 it represents the minimum wage when the recording of the data started. y-intercept is 6.50

d.) The equation is given by y - 6.50 = 0.205(x - 0)
y = 0.205x + 6.5

e.) f(x) = 0.205x + 6.5

f.) Year 2020 is 20 years after 2000, i.e. x = 20. Therefore, you will earn y = 0.205(20) + 6.5 = 4.1 + 6.5 = $10.60

1a.) Let x represent the number of years after 2000, Then the required equation is y - 1.58 = (1.27 - 1.58)/(10 - 2) (x - 2) = -0.03875(x - 2) = -0.03875x + 0.0775
y = -0.03875x + 0.0775 + 1.58 = -0.03875x + 1.6575
y =  -0.03875x + 1.6575

b.) The slope is -0.03875. It represents the amount at which the number by which the number of tickets sold is decreasing. It states that the number of tickets sold decreases by 38.75 million every year.

c.) The y-intercept is 1.6575 which represents the number of tickets sold in 2000, which is not true because the data told us that the highest ticket was sold in 2002.