NAME Interpreting Intercepts Algebra 1. One summer, you charged $20 to mow a lawn and $10 to trim bushes. You want to make $300 in one week. An algebraic model (equation) for your earnings is 20x + 10y = 300. The graph at the right is a representation of this situation. a. What is the x-intercept? What does it mean? b. What is the y-intercept? What does it mean? c. Name two other possible combinations of lawns and bushes that would earn you $300. 2. You run the 100 meter dash. The graph of d = -5t + 100 models your distance from the finish line. a. What does the variable d stand for? b. What does the variable t stand for? c. What does the ordered pair (0, 100) mean? d. What does the ordered pair (20, 0) mean? 3. You are organizing the annual spaghetti dinner to raise funds for a zoo. Your goal is to sell $1500 worth of tickets. Assuming 200 adults and 100 children will attend the dinner, how much should you charge for an adult ticket? a. Write an algebraic equation to model this situation. Explain what each variable represents. b. Graph the equation. c. What is the x-intercept? What does it mean? d. What is the y-intercept? What does it mean? e. Name three possible price combos. f. What would be the most reasonable price to charge adults and children? Why? 4. The number of people who worked for the railroads in the United States each year from 1999 to 2005 can be modeled by the equation y = -6.61x + 229, where x represents the number of years since 1989 and y represents the number of railroad employees (in thousands). a. What is the y-intercept? What does it mean? b. What is the x-intercept? What does it mean? c. Do you think the line graph will continue to be a good model for the next 50 years? Explain. 5. The Student Council is selling tickets to the fall carnival. They would like to sell $2000 worth. If the cost of a student ticket is $5 and the cost of an adult ticket is $10, how many of each kind could they sell to reach their goal? a. Write an equation to model the situation. Explain what each variable represents. b. What is the x-intercept? What does it mean? c. What is the y-intercept? What does it mean? d. All ordered pairs that lie on the line are possible solutions of your equation. Why are integer solutions the only acceptable answers to the question? e. Give two reasonable answers to the question. Graph each equation using slope-intercept form. 6. 2x + 4y = 16 7. y = -6 + 3x 8. 2x - 3y = 6