Algebra Class 10 - Linear Relations Quiz

Questions and Answers

Which of these ordered pairs are not points on the graph of $2x + 4y = 20$? Justify your decision.

(-3, 7) (correct)

(0, 5)

(12, -1) (correct)

(6, 2)

(10, 0)

How many muffins and doughnuts can Jacob buy with $15 if muffins are 75¢ each and doughnuts are 25¢ each?

Various combinations of 0-20 muffins and 0-60 doughnuts depending on allocation of budget.

What is the maximum number of muffins that Jacob can buy?

What is the maximum number of doughnuts that Jacob can buy?

60 Signup and view all the answers

Write an equation that describes Jacob's options for buying muffins and doughnuts.

0.75m + 0.25d = 15 Signup and view all the answers

Which representation do you think is more useful for Jacob, a graph or a table? Justify your choice.

This is subjective; answer may vary. Signup and view all the answers

State two ordered pairs that satisfy the linear relation $y = 5x - 1$ and one ordered pair that does not.

Satisfy: (0, -1), (1, 4); Does not satisfy: (2, 5) Signup and view all the answers

State two ordered pairs that satisfy the linear relation $3x - 4y = 24$ and one ordered pair that does not.

Satisfy: (0, -6), (8, 0); Does not satisfy: (2, 2) Signup and view all the answers

State two ordered pairs that satisfy the linear relation $y = -25x + 10$ and one ordered pair that does not.

Satisfy: (0, 10), (1, -15); Does not satisfy: (2, 30) Signup and view all the answers

State two ordered pairs that satisfy the linear relation $5x = 30 - 2y$ and one ordered pair that does not.

Satisfy: (6, 0), (0, 15); Does not satisfy: (3, 1) Signup and view all the answers

Define suitable variables for Caroline's working hours equation.

Let d = hours at day job, e = hours at evening job; Equation: d + e = 40 Signup and view all the answers

Define suitable variables and write an equation for Caroline's earnings.

Let d = hours at day job, e = hours at evening job; Equation: 15d + 11e = 540 Signup and view all the answers

Define variables and write an equation for Justin's weekly earnings.

Let s = weekly sales; Equation: Earnings = 500 + 0.06s Signup and view all the answers

Define variables and write an equation for Justin's new job offer.

Let s = weekly sales; Equation: Earnings = 800 + 0.04s Signup and view all the answers

Define suitable variables and write an equation for the piggy bank situation.

Let n = number of nickels, d = number of dimes; Equation: 0.05n + 0.10d = 5.25 Signup and view all the answers

Graph the relations in question 5, parts a) and b).

Refer to the graph showing linear relationships based on definitions. Signup and view all the answers

Should Justin take the new job if he usually has about $18,000 in weekly sales?

Yes, if $800 + 0.04(18000) > 500 + 0.06(18000) Signup and view all the answers

Create a table to show Deb's spending on calls and text messages.

Table will demonstrate possible combinations of calls and texts within $25. Signup and view all the answers

Create a graph representing Deb's potential spending on calls and text messages.

Graph illustrates the combinations on a budget line. Signup and view all the answers

Create an equation for Leah's monthly paycheck based on sales.

Earnings = 1200 + 0.035 * Sales Signup and view all the answers

Is Leah's pay before deductions of $4566.09 correct given her sales of $96,174?

No, it is not correct. Signup and view all the answers

Study Notes

Checking Understanding

Evaluate which ordered pairs satisfy the linear equation 2x + 4y = 20.
Ordered pairs in question:
- (10, 0)
- (-3, 7)
- (6, 2)
- (0, 5)
- (12, -1)

Representing Linear Relations

Jacob's budget for muffins and doughnuts is $15.
Muffins cost 0.75each,anddoughnutscost0.75 each, and doughnuts cost 0.75each,anddoughnutscost0.25 each.
Possible combinations of muffins (x) and doughnuts (y) derive from the equation: 0.75x + 0.25y ≤ 15.
Maximum muffins Jacob can buy: 20 (if he buys muffins only).
Maximum doughnuts Jacob can buy: 60 (if he buys doughnuts only).
Graphing options can visually represent combinations possible within the budget.

Practising Linear Relations

Find two ordered pairs for each linear equation:
- y = 5x - 1
  - Satisfying pairs: (0, -1), (1, 4)
  - Non-satisfying pair: (2, 5)
- 3x - 4y = 24
  - Satisfying pairs: (4, 0), (8, 6)
  - Non-satisfying pair: (0, 6)
- y = -25x + 10
  - Satisfying pairs: (0, 10), (1, -15)
  - Non-satisfying pair: (0, 20)
- 5x = 30 - 2y
  - Satisfying pairs: (6, 0), (0, 15)
  - Non-satisfying pair: (3, 1)

Defining Variables and Writing Equations

Caroline's scenarios:
- Total hours worked: x + y = 40 (where x = day job hours, y = evening job hours).
- Total earnings: 15x + 11y = 540.
Justin's earnings can be described by:
- Current job: y = 500 + 0.06x (where x is weekly sales).
- New job: y = 800 + 0.04x.
Piggy bank contains $5.25 in nickels (n) and dimes (d): 0.05n + 0.10d = 5.25.

Graphing Relations

Graph the equations derived from Caroline’s work hours and earnings.
Visual representation aids in understanding constraints and possibilities in the equations.

Analyzing Job Offers

Justin's weekly sales average around $18,000.
The decision to accept the new job should consider total earnings compared to current position after commission.

Deb's Monthly Budget

Deb pays 0.10perminuteforcalls,0.10 per minute for calls, 0.10perminuteforcalls,0.06 per text; total budget is $25.
Use a table to list combinations of calls and texts within the $25 limit.
Graphical representation of spending can show relationship between usage of calls and texts.

Leah's Earnings Evaluation

Leah earns a fixed salary plus commission: y = 1200 + 0.035x (x is sales).
Last month's sales totaled $96,174, yielding commissions to check against her reported pay.
Verify if reported pay of $4,566.09 aligns with her earnings based on actual sales and commission structure.

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Description

Test your understanding of linear equations and relationships through this quiz. You'll evaluate various ordered pairs against the equation 2x + 4y = 20 and apply practical math skills to budget for muffins and doughnuts at a bake sale.