Slope-Intercept Equations and Systems: Grade 8 Challenge

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

• Slope: 0.25, Intercept: 25

• Slope: 0.30, Intercept: 20

• Slope: 0.10, Intercept: 30

• Slope: 0.20, Intercept: 30

A local gym charges a monthly fee of $25 plus $5 for each class attended. Write the equation in slope-intercept form for the total cost (C) based on the number of classes (c) attended. Identify the slope and intercept.

• C = 20c + 25; slope = 20, intercept = 25

• C = 5c + 25; slope = 5, intercept = 25

• C = 10c + 15; slope = 10, intercept = 15

• C = 5c + 30; slope = 5, intercept = 30

Two friends are saving money for a concert. Friend A saves $10 a week, while Friend B saves $15 a week. Write a system of equations to represent their savings over time. What is the slope and intercept for each friend?

• Friend A: slope = 10, intercept = 5; Friend B: slope = 15, intercept = 5.

• Friend A: slope = 5, intercept = 0; Friend B: slope = 10, intercept = 0.

• Friend A: slope = 20, intercept = 0; Friend B: slope = 15, intercept = 10.

• Friend A: slope = 10, intercept = 0; Friend B: slope = 15, intercept = 0.

A phone plan costs $40 per month plus $0.10 per text message. Write the equation in slope-intercept form for the total cost (C) based on the number of text messages (t) sent. Identify the slope and intercept.

• C = 0.05t + 40; slope = 0.05, intercept = 40

• C = 40t + 0.10; slope = 40, intercept = 0.10

• C = 0.10t + 40; slope = 0.10, intercept = 40

• C = 0.10t + 20; slope = 0.10, intercept = 20

A bakery sells cupcakes for $3 each and cookies for $2 each. If a customer buys a total of 10 items for $24, write a system of equations to represent the situation. What are the slopes and intercepts of the equations?

• x + y = 8 and 3x + 2y = 20

• The system of equations is: x + y = 10 and 3x + 2y = 24. Slopes: -1 (first equation), -1.5 (second equation). Intercepts: 10 (first equation), 12 (second equation).

• x + y = 10 and 2x + 3y = 24

• x + y = 12 and 3x + 2y = 30

A school is selling tickets for a play. Adult tickets are $12 and student tickets are $8. If they sell a total of 50 tickets for $480, write a system of equations to represent the situation. Identify the slope and intercept for each equation.

• x + y = 50; 12x + 10y = 480; Slope and intercept for first: -1, 50; for second: -1.2, 48.

• x + y = 50; 12x + 8y = 480; Slope and intercept for first: -1, 50; for second: -1.5, 60.

• x + y = 60; 12x + 8y = 480; Slope and intercept for first: -1, 60; for second: -1.5, 50.

• x + y = 50; 10x + 8y = 480; Slope and intercept for first: -1, 50; for second: -1.25, 60.

A taxi company charges a base fare of $5 plus $2 per mile. Write the equation in slope-intercept form for the total fare (F) based on miles driven (m). What is the slope and intercept?

• Slope: 5, Intercept: 2

• Slope: 0, Intercept: 5

• Slope: 2, Intercept: 5

• Slope: 2, Intercept: 10

A gardener is planting flowers in two different types of pots. Pot A costs $4 each and Pot B costs $6 each. If the total cost for 10 pots is $50, write a system of equations to represent the situation. Identify the slopes and intercepts.

• System of equations: x + y = 10, 4x + 6y = 50; Slopes: -1 (for first), -2/3 (for second); Intercepts: 10 (for first), 25/3 (for second)

• x + y = 12, 4x + 6y = 48

• x + y = 10, 5x + 7y = 50

• x + y = 8, 4x + 6y = 40

A bookstore sells novels for $15 each and magazines for $5 each. If a customer buys a total of 20 items for $150, write a system of equations to represent the situation. What are the slopes and intercepts of the equations?

• x + y = 20 and 15x + 10y = 150; Slopes: -1 and -1.5; Intercepts: 20 and 15.

• x + y = 25 and 10x + 5y = 150; Slopes: -2 and -5; Intercepts: 25 and 30.

• x + y = 15 and 20x + 5y = 150; Slopes: -1 and -4; Intercepts: 15 and 30.

• The system of equations is: x + y = 20 and 15x + 5y = 150. Slopes: -1 and -3; Intercepts: 20 and 30.

A delivery service charges a flat fee of $10 plus $1.50 per mile. Write the equation in slope-intercept form for the total cost (C) based on miles driven (m). Identify the slope and intercept.

• C = 1.50m + 5; Slope: 1.50, Intercept: 5

• C = 10m + 1.50; Slope: 10, Intercept: 1.50

• C = 1.50m + 10; Slope: 1.50, Intercept: 10

• C = 2m + 10; Slope: 2, Intercept: 10