Grade 8 | Unit 5 | Lesson 9: Linear Models | Practice Problems

On the first day after the new moon, 2% of the Moon's surface is illuminated. On the second day, 6% is illuminated. Based on this information, predict the day on which the Moon’s surface is 50% illuminated. Is the percentage illumination of the Moon’s surface a linear function of the day?

• The Moon's surface is 50% illuminated on day 13

• The Moon's surface is 50% illuminated on day 14

• The percentage illumination is a linear function

• The percentage illumination is not a linear function

Predict the day on which the Moon's surface is 100% illuminated. Does this agree with the prediction you made?

• The Moon's surface is 100% illuminated on day 14

• It agrees with the prediction

• It does not agree with the prediction

In science class, Jada uses a graduated cylinder with water in it to measure the volume of some marbles. After dropping in 4 marbles so they are all under water, the water in the cylinder is at a height of 10 milliliters. After dropping in 6 marbles so they are all under water, the water in the cylinder is at a height of 11 milliliters. What is the volume of 1 marble?

• 0.5 ml

• 1 ml

• 1.5 ml

How much water was in the cylinder before any marbles were dropped in?

• 8 ml

• 9 ml

• 10 ml

What should be the height of the water after 13 marbles are dropped in?

• 14.5 ml

• 15 ml

• 15.5 ml

Is the relationship between volume of water and number of marbles a linear relationship? If so, what does the slope of a line representing this relationship mean? If not, explain your reasoning.

• Yes, the slope represents the volume of 1 marble

• No, the relationship is not linear

For a certain city, the high temperatures (in degrees Celsius) are plotted against the number of days after the new year. Is the high temperature in this city a linear function of the number of days after the new year?

• Yes, it fits a linear model

• No, it does not fit a linear model