Linear Models Worksheets Grade 8

1. Emma is training for a charity bike ride. She tracks her training progress and finds that the distance she can cycle in kilometers, y, after x weeks of training is modeled by the linear equation y = 15x + 20. What does the number 15 represent in this context, and what does the number 20 represent?
2. Mere runs a small catering business. The total cost C in dollars to cater for x people at an event is given by the linear equation C = 12x + 80. Interpret the meaning of the slope (12) and the y-intercept (80) in the context of this catering business.
3. The equation y = 3.75x + 12.50 models the total cost (y) in dollars for a pizza delivery based on the number of toppings (x). What does the slope represent? What does the y-intercept represent?

…and 5 more problems

1. (3x + 15) ÷ 3 = 8
2. The graph below shows the distance (in meters) a drone travels over time (in seconds). The line passes through the points (0, 27) and (7, 97). The equation of the line is y = 10x + 27. What does the slope of 10 represent in this context? What does the y-intercept of 27 represent?
3. The equation y = 6.5x + 15 represents the total cost (y) in dollars for a bicycle rental, where x is the number of hours rented. What does the slope represent? What does the y-intercept represent?

…and 5 more problems

1. Emma is training for a charity walk-a-thon. She tracks her total distance walked over several days and finds that the relationship between the number of days she has been training (x) and her total distance walked in miles (y) can be modeled by the linear equation y = 3.5x + 5. What does the number 3.5 represent in this context, and what does the number 5 represent?
2. A city's public transportation system uses the equation R = 1.75d + 2.50 to calculate the fare R in dollars for a ride based on distance d in miles. If Emma pays $9.75 for her bus ride to school, how many miles did she travel?
3. Aroha is tracking the height of a plant over time. She graphs the data and draws a line of best fit. The line passes through the points (5, 13) and (11, 25), where x represents the number of weeks since planting and y represents the height in centimeters. Write the equation of the line in slope-intercept form and interpret the meaning of the slope and the y-intercept in the context of the plant's growth.

…and 4 more problems