Applications of Slope and Intercept

This lecture series explores the meaning of slope and intercepts in the context of real-life situations. Watch the videos and complete the interactive exercises.

Relating linear contexts to graph features - Questions

1.A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. When he started his diet, he weighed $79.5$ . He gained weight at a rate of $5.5$ kilograms per month.

Let $y$ represent the sumo wrestler's weight (in kilograms) after $x$ months.

Which of the following could be the graph of the relationship?

Choose 1 answer:

2. Conrad read a $180$ -page book cover to cover in a single session, at a constant rate. It took him $6$ hours.

Let $y$ represent the number of pages left to read after $t$ hours.

Which of the following information about the graph of the relationship is given?

Choose 1 answer:

A. Slope and $x$ -intercept

B. Slope and $y$ -intercept

C. Slope and a point that is not an intercept

D. $x$ -intercept and $y$ -intercept

E. $y$ -intercept and a point that is not an intercept

F. Two points that are not intercepts

3. Nour drove from the Dead Sea up to Amman, and her altitude changed at a constant rate. When she began driving, her altitude was $400$ meters below sea level. When she arrived in Amman $2$ hours later, her altitude was $1000$ meters above sea level.

Let $y$ represent Nour's altitude (in meters) relative to sea level after $x$ hours.

Which of the following could be the graph of the relationship?

Choose 1 answer:

4. Hiro painted his room. After $3$ hours of painting at a rate of $8$ square meters per hour, he had $28$ square meters left to paint.

Let $y$ represent the area (in square meters) left to paint after $x$ hours.

Which of the following information about the graph of the relationship is given?

Choose 1 answer:

A. Slope and $x$ -intercept

B. Slope and $y$ -intercept

C. Slope and a point that is not an intercept

D. $x$ -intercept and $y$ -intercept

E. $y$ -intercept and a point that is not an intercept

F. Two points that are not intercepts

5. A charity organization had a fundraiser where each ticket was sold for a fixed price. After selling $200$ tickets, they had a net profit of $$12,000$ . They had to sell a few tickets just to cover necessary production costs of $$1,200$ .

Let $y$ represent the net profit (in dollars) when they have sold $x$ tickets.

Which of the following could be the graph of the relationship?

Choose 1 answer:

6. A charity organization had to sell $18$ tickets to their fundraiser just to cover necessary production costs. They sold each ticket for $$45$ .

Let $y$ represent the net profit (in dollars) when they have sold $x$ tickets.

Which of the following information about the graph of the relationship is given?

Choose 1 answer:

A. Slope and $x$ -intercept

B. Slope and $y$ -intercept

C. Slope and a point that is not an intercept

D. $x$ -intercept and $y$ -intercept

E. $y$ -intercept and a point that is not an intercept

F. Two points that are not intercepts

7. Mr. Mole left his burrow that lies below the ground and started digging his way at a constant rate deeper into the ground. Let $y$ represent Mr. Mole's altitude (in meters) relative to the ground after $x$ minutes.

Which of the following could be the graph of the relationship?

Choose 1 answer: