3.2D Homework: Writing Linear Equations to Solve Real-World Problems* Name:

Period:

Directions: Define your variables and write an equation to represent each problem. 2. The graph below shows the length of a boa constrictor, relating time (in weeks) since the boa constrictor’s birth to its length (in inches). The boa constrictor was 30.4 in. at 8 weeks and 49.6 in. at 32 weeks. Label the axes of the graph.

Length in inches

Altitude in Feet

1. The graph below shows the descent of an airplane, relating time (in minutes) since the plane started its descent to the altitude (in feet) of the plane. Label the axes of the graph.

Time in Minutes Time in Weeks a. Define your variables and write an equation in slope-intercept form: let x represent time in minutes let y represent altitude in feet

b. Use the graph and equation to tell the story of this airplane. An airplane starts its descent 30,000 feet above the ground. It descends at a constant rate of 500 feet per minute.

c. How long it will take for the airplane to reach the ground at this rate? It will take 60 minutes or 1 hour

a. Define your variables and write an equation in slope intercept form: let x represent time in weeks let y represent length in inches

b. Use the graph and equation to tell the story of this boa constrictor. This boa constrictor is 24 inches in length at birth. It grows 0.8 inches per week.

c. How long will the boa constrictor be at one year if it continues to grow at this rate? It will be 65.6 inches long.

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3. The table below shows the amount of money Lance has in his savings account where x is time (in months) and y is the account balance (in dollars). x (time) 0 3 6 9

y (account balance) 160 385 610 835

a. Define your variables and write an equation in slopeintercept form: let x represent time in months let y represent account balance in dollars b. Use the table and equation to tell the story of Lance’s savings. Lance starts with $160 in his account and saves $75 per month. c. If Lance continues to save at this rate, about how long will it take for him to have $2,000? It will take about 25 months.

4. Elizabeth charges $30 for a 30 minute guitar lesson. Before working with a new student, Elizabeth requires them to purchase a “Beginner’s Guitar” book. Yesterday, Elizabeth charged her new student $70 for a one hour lesson. a. Define your variables and write an equation in slope-intercept form: let x represent time in hours let y represent cost in dollars

Teacher note: The charge is $30 for 30 minutes, not hours, therefore it costs $60 per hour.

b. Use your equation to add more details to the story about the price for the “Beginner’s Guitar” book. The cost of the “Beginner’s Guitar” book is $10.

c. How much would Elizabeth charge a new student for a three hour lesson? $190

5. The cost to rent a jet ski is $80 per hour. The cost also includes a flat fee for a lesson on how to use the jet ski. Steve rented a jet ski for 3 hours and the total bill was $265. a. Define your variables and write an equation in slope-intercept form: let x represent time in hours let y represent cost in dollars

b. Use your equation to add more details to the story about renting a jet ski. The initial fee of renting a jet ski (cost of the lesson) is $25.

c. How much would it cost to rent a jet ski for 8 hours? $665

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6. The cost of a party at Jumpy Jumps is $250 which includes cake, pizza, and admission for any number of children. Create the graph and equation that represents this situation where x is the number of children and y is the total cost. a. Equation: b. What is the slope of your line? zero

c. Change the context of the situation to represent a graph with positive slope.

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