Mastering Standard Form: Graphing Linear Equations

A local bakery sells cupcakes for $2 each and cookies for $1 each. If the total revenue from selling 50 items is $80, write an equation in standard form to represent the relationship between the number of cupcakes (x) and cookies (y).

• 3x + y = 80

• 2x + y = 80

• x + 2y = 80

• 2x + 3y = 80

Convert the equation 2x + y = 80 into standard form and identify the x-intercept and y-intercept. What do these intercepts represent in the context of the bakery?

• Standard form: x + 2y = 80; x-intercept: (0, 80); y-intercept: (40, 0).

• Standard form: 2x + y = 100; x-intercept: (50, 0); y-intercept: (0, 100).

• Standard form: 2x + y = 60; x-intercept: (30, 0); y-intercept: (0, 60).

• Standard form: 2x + y = 80; x-intercept: (40, 0); y-intercept: (0, 80).

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write a linear equation in standard form to represent the total cost (C) as a function of miles driven (m).

• C = 30 + 0.20m

• 20m - C = -3000

• C = 30m + 20

• C = 0.20m - 30

Graph the equation 0.2m + C = 30. What does the slope of the line represent in this scenario?

• The slope of the line represents the rate of change of C with respect to m, specifically that C decreases by 0.2 for each unit increase in m.

• The slope represents the maximum value of C in the equation.

• The slope shows that C increases by 0.2 for each unit increase in m.

• The slope indicates the total value of C when m is zero.

A school is planning a field trip and has a budget of $500. The cost per student is $25. Write an equation in standard form to represent the maximum number of students (s) that can attend the trip.

• 20s - 500 = 0

• 30s - 500 = 0

• 25s + 500 = 0

• 25s - 500 = 0

A farmer has a total of 100 acres of land to plant corn and wheat. If he plants corn on x acres and wheat on y acres, write an equation in standard form to represent the total land available.

• x + y = 100

• x - y = 100

• 2x + 3y = 100

• x + y = 50

Graph the equation x + y = 100. What do the points on the line represent in terms of land allocation?

• The points on the line show the cost of land per unit.

• The points on the line indicate the maximum yield of crops from the land.

• The points on the line represent the total area of land available.

• The points on the line represent different combinations of land allocation between two types of land, totaling 100 units.

A concert venue has a seating capacity of 2000. If tickets are sold for $50 each and the total revenue is $80,000, write an equation in standard form to represent the relationship between the number of tickets sold (t) and the total revenue (R).

• R - 50t = 0

• R = 50t + 20,000

• 50t - R = 0

• 50t + R = 80,000

Convert the equation 50t = 80000 into standard form and determine how many tickets need to be sold to reach the revenue goal. What does this tell you about ticket sales?

• 1200 tickets

• 1600 tickets

• 800 tickets

• 2000 tickets