Constant Rates
5, 7, 11, 17, 25...
Rana is taking the taxi to her appointment. The taxi charges $5.50 for the first kilometre. Each additional kilometre is $2.50. Using a table of values as needed, write an equation that represents the rule.
Let x represent the distance and y represent the cost.
y = 2.5x + 3
If x = 14, what is the product of 3x + 4 (8 - 2)?
If x = 14, then the product is 66.
< means...?
Fewer than, less than, below
How can you tell that a pattern is linear?
It increases through addition or decreases through subtraction the same amount every time. When graphed, it will appear in a straight line.
A series of figures are depicted for a classroom. Shape 1 is made up of a single square. Shape two is made up of three squares. Shape three is made up of five squares. How many squares would be in Figure 72?
143 squares would be in Figure 72.
Is t=7 a solution to t2+3t−10=4+8t?
True or false: when you want to show inequalities on a number line, a white dot with a black outline refers to an inequality that could be greater than/less than as well as equal to?
False. When a dot is fully shaded in black, that is when we know it also includes "equal to". A white dot means that it is either going to be greater than or less than alone.
Are all constant rates going to graph as linear patterns?
Yes, because linear patterns are increasing or decreasing by the same amount every time.
A table consists of the following values....
Input Output
1 8
2 12
3 16
Write a pattern rule for this table of values.
The pattern rule for this particular table of values is 4x + 4
If x = 6, then what is the answer for 2x−5=3(1−x)+22?
x = 7
Below are a series of numbers that you can plug into the equation x > -15. Which of these numbers creates a true statement?
-15, -8, 12, -17
The numbers that create a true statement are -8 and 12.
Kyrie is part of a soccer house league. There are 6 teams in her division. Those 6 teams must play each team once. How many games will there be in total for the season?
There will be 15 games if there are 6 teams.
Kasia is saving up to buy a new computer screen. She is saving $20 a week. How many weeks will it take her to save at least $250?
She would need to wait approximately 13 weeks to have saved up $250 (rounding).
Consecutive numbers are numbers that continuously follow each other, such as 3 and 4. The sum of two consecutive numbers is 181. Let n be the first number. What are the two numbers?
Let n be the one number, and let n + 1 be the other number.
n + n + 1 = 181
2n + 1 = 181
2n = 180
n = 90
90 + 91 = 181
Therefore, the numbers are 90 + 91.
Jillian and Jasmine are playing on a basketball team together. Jillian scores x points and Jasmine scores y points. Together, they score less than 10 points. Write an inequality to show this relationship.
x and y both have to be less than 10 points, so x + y < 10 shows the relationship between the points.
What is a recursive pattern rule?
Tells you the start of a pattern and how to continue (Example: "Start with 3, then add 3 each time.")
What is the explicit pattern rule?
Uses the term number to determine a term in the pattern (EXAMPLE: "Multiply the term number by 3").
Peter’s salary is twice Ann’s salary and half of David’s salary. Then the average salary of Ann and David is _____________ Peter’s salary. (Equal to, larger than, lesser than)
Larger than
If you were to graph the following inequality on a number line, would it go up or down?
y < 3x + 1
The graphed version of the inequality y < 3x + 1 would go up.