Interpreting Slope and Y-intercept

Interpreting Slope and Y-intercept

Read each question carefully and provide a clear, concise answer. Show all your work for full credit.

1. The equation y = 3x + 5 represents the cost (y) of a taxi ride for 'x' miles. What does the slope of this equation represent in the context of the taxi ride?

2. A linear function models the amount of water in a tank over time. If the slope is -10 gallons/minute, what does this tell you about the water in the tank?

3. In the equation y = 3x + 5 from Question 1, what does the y-intercept represent in the context of the taxi ride?

4. A plant's height (in cm) over time (in weeks) is modeled by a linear equation. If the y-intercept is 15 cm, what does this indicate about the plant?

5. The graph below shows the distance (y) a car travels over time (x). What is the most appropriate interpretation of the slope of this line?

6. For the same graph in Question 5, what does the y-intercept represent?

7. A linear model for the temperature of a cooling cup of coffee is T = -2t + 90, where T is the temperature in Celsius and t is the time in minutes. The slope indicates that the coffee's temperature   by 2 degrees Celsius every  .

8. In the equation C = 2.50 + 0.75n, representing the cost (C) of renting a bike for 'n' hours, the y-intercept of 2.50 represents the  , while the slope of 0.75 represents the  .

9. If the slope of a line is positive, it means that as the x-value increases, the y-value decreases.

10. The y-intercept always represents the starting value or initial condition in a real-world problem.