Exploring Linear Functions and Proportionality

What is the standard form of a linear equation discussed in the lesson?

• x = my + b

• y = bx + m

• y = mx + b

• y = mx + c

What does the 'm' in the linear equation y = mx + b represent?

• Maximum value of y

• Slope or rate of change

• X-intercept

• Y-intercept

Is the cost of bags of candy an example of a linear function?

• No, as the cost is not related to the number of bags

• Yes, as the cost increases by a constant amount

• No, as the cost decreases over time

• Yes, but only during promotions

Which scenario describes a non-linear function?

• Cost increases by a fixed amount per bag of candy

• Price per bag remains unchanged

• Buy four bags, get one at 50% off

• Constant rate of water flow into a tub

How many gallons per minute does the water flow into the bathtub?

• 3.5 gallons per minute

• 7 gallons per two minutes

• 3.5 gallons per two minutes

• 7 gallons per minute

What is the y-intercept in the context of the bathtub filling example?

• Initial volume of water in the tub

• Total time to fill the tub

• Rate of water flow

• None, as the tub starts empty

What is the new filling time for the bathtub if it starts with 8 gallons of water?

• 12 minutes

• 14.3 minutes

• 14 minutes

• 10 minutes

How does the initial condition of water in the tub affect the filling time?

• No effect

• Increases the time

• Decreases the time

• Varies unpredictably

How long was the faucet running before it was noticed, based on the initial 6 gallons in the tub?

• 10 minutes

• 6 minutes

• 3 minutes

• 5 minutes

What method is used to verify the rate of water flow in the final example?

• Subtraction of initial and final volumes

• Calculation of slope from table values

• Multiplication of rate by time

• Estimation based on visual inspection