Interpreting Slope and Y-intercept Worksheet
Grade 12 math worksheet on interpreting slope and y-intercept in linear equations and real-world contexts.
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Interpreting Slope and Y-intercept
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Read each question carefully and provide detailed answers, showing all work where applicable. Interpret the meaning of slope and y-intercept in the given contexts.
1. The cost of producing 'x' units of a product is given by the linear equation C = 15x + 200. What does the slope of this equation represent in this context? Explain your reasoning.
2. In the equation C = 15x + 200 from Question 1, what does the y-intercept represent? Explain its significance to the company.
3. A linear model for the temperature (T, in °C) in a refrigerator 'h' hours after a power outage is T = 0.5h + 4. The slope is , which means the temperature . The y-intercept is , which means the initial temperature when the power went out was .
4. A car's fuel efficiency is modeled by the equation y = -0.05x + 20, where 'y' is the amount of fuel remaining in gallons and 'x' is the distance driven in miles. Which of the following is the correct interpretation of the slope?
The car uses 0.05 gallons of fuel per mile.
The car starts with 0.05 gallons of fuel.
The car travels 0.05 miles per gallon.
The car has 20 gallons of fuel after 0.05 miles.
5. If a linear equation modeling population growth has a negative slope, it means the population is increasing over time.
True
False
6. Consider a graph where the x-axis represents the number of hours studied and the y-axis represents a student's test score. If the line passes through the point (0, 60) and has a slope of 5, what do these values mean in terms of the student's performance?
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