Slope and Intercept in Real-Life Systems of Equations

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write the equation for the total cost (C) in terms of miles driven (m). What is the slope and y-intercept?

• C = 30 + 0.20m; Slope: 30, Y-intercept: 0

• C = 30 + 0.20m; Slope: 0.20, Y-intercept: 30

• C = 20 + 0.20m; Slope: 0.20, Y-intercept: 20

• C = 30 + 0.50m; Slope: 0.50, Y-intercept: 30

A local gym offers a membership for $50 plus $10 per class attended. Write the equation for the total cost (C) in terms of classes attended (c). Identify the slope and intercept.

• C = 40 + 10c; Slope: 10, Intercept: 40

• C = 50 + 15c; Slope: 15, Intercept: 50

• C = 50 + 5c; Slope: 5, Intercept: 50

• C = 50 + 10c; Slope: 10, Intercept: 50

Two friends are saving money for a concert. Friend A saves $5 a week, while Friend B saves $10 a week. Write a system of equations to represent their savings over time. What is the slope for each friend?

• A(t) = 5t + 2, B(t) = 10t + 2; Slope A = 5, Slope B = 10

• A(t) = 5t, B(t) = 10t; Slope A = 5, Slope B = 10

• A(t) = 10t, B(t) = 5t; Slope A = 10, Slope B = 5

• A(t) = 5t, B(t) = 15t; Slope A = 5, Slope B = 15

A store sells pencils for $0.50 each and erasers for $1.00 each. If a student buys a total of 10 items for $6.00, write a system of equations to represent this situation. Identify the slope and intercept of each equation.

• x + y = 5 and 0.5x + 2y = 6

• System of equations: x + y = 10 and 0.5x + y = 6; Slope and intercept: First equation (slope = -1, intercept = 10), Second equation (slope = -0.5, intercept = 6)

• 2x + y = 10 and 0.5x + 2y = 6

• x + 2y = 10 and 0.5x + y = 5

A taxi charges a base fare of $2.50 plus $1.50 per mile. Write the equation for the total fare (F) in terms of miles (m). What is the slope and y-intercept?

• F = 2.50 + 1.50m; Slope: 1.50, Y-intercept: 2.50

• F = 2.50m + 1.50; Slope: 2.50, Y-intercept: 1.50

• F = 2.50 + 2.00m; Slope: 2.00, Y-intercept: 2.50

• F = 1.50m; Slope: 2.50, Y-intercept: 1.50

A school is selling tickets for a play. Adult tickets cost $8 and student tickets cost $5. If they sold a total of 100 tickets for $680, write a system of equations to represent this situation. Identify the slope and intercept.

• x + y = 120; 8x + 5y = 700; Slope = -5/8, Intercept = 120.

• x + y = 80; 8x + 5y = 600; Slope = -5/8, Intercept = 80.

• x + y = 100; 7x + 6y = 680; Slope = -7/6, Intercept = 100.

• x + y = 100; 8x + 5y = 680; Slope = -8/5, Intercept = 100.

A gardener is planting flowers in two types of pots. Pot A holds 3 flowers and costs $4, while Pot B holds 5 flowers and costs $6. Write a system of equations to represent the total number of flowers and cost. What are the slopes?

• Slopes are 0 for flowers and 1 for cost.

• Slopes are -3/5 for flowers and -2/3 for cost.

• Slopes are 3/5 for flowers and 2/3 for cost.

• Slopes are -1/2 for flowers and -4/5 for cost.

A phone plan charges a monthly fee of $25 plus $0.10 per text message. Write the equation for the total cost (C) in terms of text messages (t). Identify the slope and intercept.

• C = 25 + 0.10t; Slope: 0.10, Intercept: 25

• C = 25 + 0.05t; Slope: 0.05, Intercept: 25

• C = 25 + 0.20t; Slope: 0.20, Intercept: 25

• C = 30 + 0.10t; Slope: 0.10, Intercept: 30

A bakery sells cupcakes for $2 each and cookies for $1 each. If a customer buys a total of 12 items for $20, write a system of equations to represent this situation. Identify the slope and intercept of each equation.

• x + y = 12; 2x + y = 15; Slope of first equation: -1, Intercept: 12; Slope of second equation: -1.5, Intercept: 15.

• x + y = 10; 2x + y = 18; Slope of first equation: -1, Intercept: 10; Slope of second equation: -2, Intercept: 18.

• x + y = 15; 2x + y = 25; Slope of first equation: -1, Intercept: 15; Slope of second equation: -2, Intercept: 25.

• x + y = 12; 2x + y = 20; Slope of first equation: -1, Intercept: 12; Slope of second equation: -2, Intercept: 20.

A student is saving money for a new laptop. They save $15 a week from their allowance and $10 a week from their job. Write a system of equations to represent their savings over time. What is the slope for each source of income?

• The slope for the allowance is 10, and for the job is 15.

• The slope for the allowance is 5, and for the job is 20.

• The slope for the allowance is 0, and for the job is 10.

• The slope for the allowance is 15, and for the job is 10.