Construct Linear Functions Worksheets Grade 9

1. Aroha is tracking the cost of a gym membership. The membership has an initial registration fee and a fixed monthly charge. After 4 months, the total cost is $260. After 9 months, the total cost is $460. Assuming the total cost increases linearly with the number of months, write a linear function C(m) that gives the total cost after m months. Then use your function to find the total cost after 15 months.
2. A local tech startup is analyzing their app's user growth. They found that the number of users follows the function f(x) = 1200(1.08)^x, where x represents months since launch. Meanwhile, their revenue is modeled by g(x) = 25x + 500. If they want to calculate the revenue per user after x months, what composite function would represent this relationship?
3. Points (5, 13) and (9, 29). Find f(x) = mx + b.

…and 3 more problems

1. A research scientist is studying the decay of a radioactive isotope. The remaining mass M(t) in grams after t days is modeled by the function M(t) = 80 × (1/2)^(t/15). The scientist needs to determine after how many days only 10 grams of the isotope will remain. Find the time t when this occurs.
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (4,0), and (4,3). A line representing the function f(x) is drawn along the hypotenuse of this triangle. What is the equation of this linear function in slope-intercept form?
3. Isabella is tracking the growth of her savings over time. She starts with a certain amount in her bank account and adds the same fixed amount each week. After 4 weeks, she has $260. After 9 weeks, she has $410. Determine the linear function S(w) that models the total amount of money in her account after w weeks, and use it to find how much money she initially had in the account.

…and 5 more problems

1. Mere is tracking the growth of a native tree species for a science project. She measures the tree's height at two different times. At the start of her observation (month 0), the tree is 12 centimeters tall. After 5 months, the tree has grown to 42 centimeters tall. Assuming the tree grows at a constant rate, construct a linear function H(t) that models the height of the tree in centimeters after t months. Then, use this function to predict the height of the tree after 8 months.
2. Mason is tracking the cost of renting a bicycle from a local shop. The shop charges a fixed initial fee plus a constant rate per hour. After 4 hours, the total cost is $26. After 9 hours, the total cost is $46. Determine the linear function C(h) that models the total cost in dollars as a function of the number of hours h rented. Then use this function to find the total cost for renting the bicycle for 12 hours.
3. Isabella is monitoring the water level in a reservoir during a drought. At 8:00 AM, the water level is 87 centimeters above the critical low mark. At 2:00 PM (6 hours later), the water level has dropped to 69 centimeters above the critical low mark. Assuming the water level decreases at a constant rate, write a linear function L(t) that models the water level in centimeters above the critical mark t hours after 8:00 AM. Then, use your function to predict how many hours after 8:00 AM the water level will reach the critical low mark (0 cm).

…and 3 more problems