Construct Linear Functions Worksheets Grade 9

1. Mason is saving money to buy a new laptop. He currently has $120 in his savings account and plans to add a fixed amount of money each week from his part-time job. After 4 weeks, he has $220. After 10 weeks, he has $370. Write a linear function f(w) that represents the total amount of money Mason has saved after w weeks, and then use it to determine how many weeks it will take for him to have $520.
2. A tech startup is modeling their user growth with the function f(x) = 2x² - 12x + 20, where x represents months since launch and f(x) represents thousands of users. The company wants to determine when their user base will reach its minimum point and how many users they'll have at that time. Find the vertex of this quadratic function.
3. f(x) = 3x² - 5x + 2, f(4) = ?

…and 4 more problems

1. 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).
2. Aroha is tracking the growth of a rare fern in her backyard. She measures the height of the fern at two different times. After 3 weeks, the fern is 15 cm tall. After 7 weeks, the fern is 27 cm tall. Assuming the fern grows at a constant rate, write a linear function h(t) that gives the height of the fern in centimeters after t weeks. Use your function to predict the height of the fern after 11 weeks.
3. Emma is analyzing the fuel efficiency of a delivery truck. The graph shows the relationship between the number of gallons of fuel used (x) and the distance traveled in miles (y). The line on the graph passes through the points (0, 0) and (25, 400). What is the linear function f(x) that models this relationship, representing the distance traveled for a given number of gallons of fuel used?

…and 3 more problems

1. Points (11, 47) and (17, 83). Find f(x) = mx + b.
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (4,0), and (4,3). A line is drawn from the vertex at (4,3) perpendicular to the hypotenuse, intersecting it at point P. What are the coordinates of point P?
3. Points (12, 47) and (20, 71). Find f(x) = mx + b.

…and 5 more problems