Linear Functions and Fuel Consumption

This video tutorial covers grade 8 module 6 on linear functions, focusing on lesson 3 about representing lines. It explains how to model situations using linear equations, graphing them based on given rates of change and initial values. The tutorial includes two exit card problems: one on car fuel consumption and another on Andrew's earnings, demonstrating how to apply linear functions to real-world scenarios.

What is the general form of a linear function?

• y = a/x + b

• y = ax + b^2

• y = ax^2 + bx + c

• y = a + bx

How can the initial value 'a' be interpreted in the context of a linear function?

• It is the x-intercept of the line.

• It is the y-intercept of the line.

• It is the slope of the line.

• It is the rate of change.

What does the graph of a linear function represent?

• A parabola that opens upwards.

• A line that passes through the given ordered pairs.

• A line that passes through the origin.

• A curve that passes through all given points.

If a car starts with 18 gallons of fuel and consumes 0.04 gallons per mile, how much fuel is left after 50 miles?

• 20 gallons

• 14 gallons

• 18 gallons

• 16 gallons

What is the rate of change in the car fuel problem?

• 4 gallons per mile

• 0.4 gallons per mile

• 0.04 gallons per mile

• 0.004 gallons per mile

How is the point (50, 16) derived in the car fuel problem?

• By calculating the fuel left after 50 miles.

• By calculating the fuel left after 75 miles.

• By calculating the fuel left after 25 miles.

• By calculating the fuel left after 100 miles.

What is the linear function that models the car's fuel consumption?

• a = 18 - 0.04M

• a = 18 + 0.04M

• a = 0.04M + 18

• a = 0.04M - 18

If Andrew works for 7 hours, how much does he earn?

• $64

• $96

• $56

• $80

How many hours does Andrew need to work to earn $64?

• 5 hours

• 3 hours

• 7 hours

• 4 hours

What is the rate of change in Andrew's earnings problem?

• $12 per hour

• $8 per hour

• $6 per hour

• $10 per hour