Y = mx + b
Minds On
Green Card / Red Card�For each of the questions that follow, hold up either your green card or your red card.�
If you agree with the statement hold up the green card, if you disagree with the statement hold up the red card.
Points
Point A is at (3, -2)
True
Point B is at (2, -1)
False (-1, 2)
B
A
Rate of Change
The rate of change is $25/week
False! The rate of change is -$25/week
Amount in Account
Number of weeks
Initial Value
The initial value is $200
True! At x=0, the value is $200
Amount in Account
Number of weeks
Independent Variable
The independent variable is Amount in Account
False! The Amount in the Account depends on the number of weeks
Amount in Account
Number of weeks
Pizza Math
A large cheese pizza at Pizza King costs $21. Each additional topping is $1.25.
The rate of change is $21
False - The rate is for each additional topping added to the pizza.
Pizza Math
A large cheese pizza at Pizza King costs $21. Each additional topping is $1.25.
A pepperoni, bacon, mushroom and cheese pizza costs $24.75.
True - Price = $21 + 3x$1.25 = $21 + $3.75 = $24.75
Pizza Math
A large cheese pizza at Pizza King costs $21. Each additional topping is $1.25.
The rate of change is $1.25
False - The rate of change is $1.25 per additional topping.
Rivalry!
Queen Pizza has a different pricing plan:
The rate of change is $2.15
True - The values in the right column go up by $2.10 each time the number of toppings increases.
Number of Toppings | Cost of a Large Pizza ($) |
0 | 16.00 |
1 | 18.15 |
2 | 20.30 |
3 | 22.45 |
4 | 24.60 |
Rivalry!
Queen Pizza has a different pricing plan:
The dependent variable is the price (in $)
True - The cost of a large pizza depends on the number of toppings.
Number of Toppings | Cost of a Large Pizza ($) |
0 | 16.00 |
1 | 18.15 |
2 | 20.30 |
3 | 22.45 |
4 | 24.60 |
The meaning of m
We already know that in a linear relationships a pattern will form. That pattern is the rate of change.
+2
+2
+2
+2
Pattern: Up by 2.
Equation: y = 2x + 8
x | y |
-2 | 4 |
-1 | 6 |
0 | 8 |
1 | 10 |
2 | 12 |
The meaning of m
What is the pattern?
-3
-3
-3
-3
Pattern: Down by 3.
Equation: y = -3x + 1
x | y |
-2 | 7 |
-1 | 4 |
0 | 1 |
1 | -2 |
2 | -5 |
The meaning of m
rise?
2
run?
3
slope?
2
3
rise
run
(0, 0)
(3, 2)
equation?
y = x
2
3
The meaning of m
rise?
4
run?
-2
slope?
4
-2
rise
run
(0, 0)
(4, -2)
equation?
y = x
4
-2
y = -2x
Always reduce your fractions
Recap! (What does m represent?)
run
The meaning of b
When examining this table, something should pop out to us.
When x = 0, y = 8, and the equation has +8 in it.
Equation: y = 2x + 8
x | y |
-2 | 4 |
-1 | 6 |
0 | 8 |
1 | 10 |
2 | 12 |
The meaning of b
The same thing happens here.
When x = 0, y = 1, and the equation has +1 in it.
Equation: y = -3x + 1
x | y |
-2 | 7 |
-1 | 4 |
0 | 1 |
1 | -2 |
2 | -5 |
m =
Recap (what does the b represent?)
Practice Time!