Activities

1. Aurora’s bank account grows according to the equation s = 30w + 100, where s is her total savings based on the number of weeks (w) that she is working. What does it mean that the point (3, 190) is a point on this line?

2. Tasha says that the linear equation y = 3x – 4 has the following four solutions: (3, 5), (0, -4), (-2, 2) and (-5, -19). You realize that one of these is not a solution. Which one is not on the line?

3. A giant pumpkin you are growing for the state fair grows according to the equation w = 1.5d + 10, where w is the pumpkins weight in pounds after growing d days since July 1^st. What are three solutions to this equation?

4. If a dogs weight is changing according to the equation w = 2.5m + 6, what is the weight of the dog (w), in pounds, after 13 months (m)?

5. The elevation of a mountain increases according to the linear equation h = 450t + 2,000, where h is the elevation above sea level in feet and t is the time in hours spent walking up the mountain. What does the coordinate point (10, 6500) mean in this situation?

6. A lemonade stand is trying to determine the profit they are making per gallon of lemonade they sell. The equation p = 2.25g – 1.50g can be used to determine the profit (p) based on the number of gallons (g) of lemonade they sell. What does it mean that the point (10, 7.50) is on this line?

7. Miguel is building cutting boards to sell at a local craft fair. He first builds three prototypes to determine what the cutting boards will look like and how long they take to build. Miguel then uses the equation b = 0.75h + 3 to determine how many cutting boards he can build (b) based on the number of hours he works (h). What does it mean that the point (8, 6) is a solution to this linear equation?

8. The amount of debt a certain college student is accruing can be modeled by the equation d = -150m – 5000, where d represents the total debt in dollars and m is the number of months since starting their sophomore year of college. What does the point (0, -5000) represent in this situation?

9. If Brian downloads two songs per day since the purchase of his new cell phone, and he has 1463 songs, 700 days after the purchase, how many songs were on the phone originally?

10. The equation m = 15w – 300 is used to describe how Carl is planning on paying off a new TV. The variable w represents the amount of weeks since the purchase of the TV and m describes the amount of money Carl still needs to pay for the TV. Why does the coordinate point (21, 15) not make sense, even though it is on the line, in this situation?

11. Tax is assessed in Pennsylvania at the 6% state sales tax rate. The equation c = 1.06p can be used to describe the total cost of an item (c), based on the original price (p). How many solutions are there to this equation?

12. Nate is very interested in President Abraham Lincoln. So much so that he would like to determine how old President Lincoln would be if he were still alive. Nate uses the equation A = Y – 1809. What does the coordinate point (2050, 241) describe in this situation?

13. The number of views of a certain viral video are increasing at a rate of v = 250,000m + 500,000 where v describes the number of views based on the number of months (m) since January. What does the input 3 and output 1,250,000 represent in this context?

14. A group of eleven friends goes to a local ice cream shop after school one spring day. The equation 2.25c + 3.15m = 30.15 represents your purchases of c ice cream cones and m milkshakes. What does the solution (5, 6) represent in this context?

15. The school band is growing at a rate of m = 3y + 51 where m is the number of current members based on the year since 2014 (y). What does the solution (-2, 45) represent in this situation?

16. Given the linear equation , find a solution to the equation that is between (3, -1) and  ?

17. A linear function describes the growth of a person (g) based on their age (a). The equation for a certain person in their mid 30’s is g = 71. What does the coordinate point (37, 71) represent in this situation?

18. A group of eleven friends goes to a local ice cream shop after school one spring day. The equation 5c + 6m = 25 represents your purchases of 5 ice cream cones and 6 milkshakes. What does the solution (2, 2.5) represent in this context?

19. The equation 0.1d – 30 = -0.25q represents the number of dimes (d) and quarters (q) that could be added together to total $30.00. Why does the solution (101, 79.6) not make sense in this situation?

20. Given the equation 1.5x – 3y = 12, what is the value of y when (y, y) is a solution to the equation?
    
    
21. How many solutions are there between point A and B on the linear equation graphed below.

22. A linear function determines the mass of an object (m) based on its volume (v), when given the constant value for it’s density (d) using the equation m = vd. What is the density of the material when 10.38 centimeters cubed is in the domain and15.57 grams is in the range of the function?

23. A math teacher likes to trick his students. He says, “Twice a number increased by six is the same as the sum of a number and three, doubled.” He then asks them to find the number that works in this equation. What should their “solution” be?

24. A group of 19 people, including you, went to a local coffee shop for breakfast. The equation 1.50c + 2t = 27.5, where c represents cups of coffee and t represents cups of tea. If the solution (7, 9) is on the line, what did everyone order to drink?

25. The table below displays the average population of a city based on the number of restaurants located in the city.

The equation y = 453x – 132288 can be used to describe the linear equation created by this table. What do the x and y variables represent in this situation?

Answer Key/Rubric

1. Three weeks after starting to work Aurora has saved $190.00

2. (-2, 2)

3. Various answers including:  (0, 10), (1, 11.5), (20, 40)

4. When the dog is 13 months old it will weigh 38.5 pounds

5. After 10 hours of walking up the mountain the climber is at 6,500 feet of elevation

6. By selling 10 gallons of lemonade, they will make $7.50 in profit

7. In 8 hours of work Miguel will have a total of 6 cutting boards (including the 3 prototypes

8. The student started their sophomore year of college with $5,000.00 in debt, or -5000 is the y-intercept of this equation

9. 63 songs

10. Carl should pay off the TV in 20 weeks, which means his last payment should be the point (20, 0) where there is no more money to pay off. The point (21, -15) would mean another payment was made after the TV was paid off

11. Although you cannot have a negative input into this function, there are still an infinite amount of positive values that you could input into this function. That means there are also an infinite amount of outputs and thus an infinite amount of solutions.

12. In the year 2050, President Lincoln would be 241 years old.

13. By April the video was viewed 1,250,000 times

14. 5 friends purchased ice cream cones and the other six purchased milkshakes

15. In the year 2012 there were only 45 members in the band

16. Various answers including

17. When the person is 37 years old they are still 71 inches tall. This is a horizontal line with 0 slope since the person is not growing taller during their 30’s.

18. Ice cream cones cost $2.00 each and milkshakes cost $2.50 each

19. The solution (101, 79.6) does not make sense because although you can have 101 dimes, you cannot have 79.6 quarters (there is no such thing as 0.6 of a quarter).

20. y = -8

21. Infinite solutions

22. Density = 1.5g/cm³

23. Any number works in this sentence, there are infinite solutions

24. 7 people order tea, 9 people order coffee and 3 people get water for free

25. The x variable represents the number of restaurants in the city and y represents the number of people in the city