Variables
What does the "m" represent in a linear equation?
The rate of change, or slope.
What is the equation for a linear pattern?
y = mx + b
y = 5x + 30
Find the value for y, when x = 8.
y = 5(8) + 30
y = 40 + 30
y = 70
A new phone costs $500, plus $14 a month for the phone plan. Create a linear equation to represent the total cost.
y = 14x + 500
A party size pizza costs $24, and each dipping sauce adds $2.
1. Write the linear equation to represent the total cost.
2. Determine the total cost if we order 13 dips.
1. y = 2x + 24
2. y = 2(13) + 24
y = 26 + 24
y = 50 The order will cost $50.
What does the "b" represent in a linear equation?
The initial value, or where the pattern begins when x = 0.
y = 7x + 11
What is the initial value?
11
y = 2x + 13
Find the value for y, when x = 9.
y = 2(9) + 13
y = 18 + 13
y = 31
Ms. Hickey bought a new pair of glasses for $180, and some boxes of contact lenses for $20 each. Create a linear equation to represent the total cost.
y = 20x + 180
The prize bin container cost Ms. Hickey $6, and each prize cost her $1.25.
1. Write the linear equation to represent the total cost.
2. Determine the total cost if there are 16 prizes.
1. y = 1.25x + 6
2. y = 1.25(16) + 6
y = 20 + 6
y = 26 The total cost is $26.
What does the "y" represent in a linear equation?
The outcome, the total being calculated or determined by x.
y = 12x - 100
Is this a shrinking or growing pattern?
Growing. m = 12, a positive number
y = 15x - 9
Find the value for y, when x = 3.
y = 15(3) - 9
y = 45 - 9
y = 36
Issie borrowed money to buy a Leafs ticket for $360. He's paying it back $20 per week. Create a linear equation to represent Issie's balance.
y = 20x - 360
A new Playstation console costs $575, plus $10 every month for Playstation Plus.
1. Write the linear equation to represent the total cost.
2. Determine the total cost after 8 months.
1. y = 10x + 575
2. y = 10(8) + 575
y = 10(8) + 575
y = 80 + 575
y = 655 The total cost after 8 months is $655.
What does the "x" represent in a linear equation?
The term number, the variable that controls the outcome being calculated.
y = -5x + 18
Is this a shrinking or growing pattern?
Shrinking. The rate of change, or m, is -5.
y = 25x + 225
Find the value for y, when x = 5.
y = 25(5) + 225
y = 125 + 225
y = 350
The temperature on Jan 1 was -5. It continued to drop 2 degrees lower each day. Create a linear equation to represent the temperature.
y = -2x - 5
A debt of $4,000 is owed to the bank, and gets payed back $150 each month.
1. Write the linear equation to represent the balance.
2. Determine the balance after 6 months.
1. y = 150x - 4000
2. y = 150(6) - 4000
y = 900 - 4000
y = 3100 The balance is -$3,100.
What does it mean if the value for m is a negative integer?
Create a growing pattern that has an initial value of an odd, negative number.
y = mx - b
As long as b is an odd number (ends in 1, 3, 5, 7, or 9)
y = -4x + 12
Find the value for y, when x = 6
y = -4(6) + 12
y = -24 + 12
y = -12
The class earned 8 everyone points, plus everyone could earn 1 point for each sudoku they solved. Create a linear equation to represent the number of points earned.
y = x + 8
Kineret wins the lottery, and wins $100,000. She decides to going on a shopping spree every weekend, spending $4,500 each time.
1. Write the linear equation to represent the lottery winnings.
2. Determine the winnings left after 9 weekends.
1. y = -4500x + 100,000
2. y = -4500(9) + 100,000
y = -40,500 + 100,000
y = 59,500 She has $59,000 left.