Quick Start Expectations1. Fill in planner and HWRS
HW: None! 2. Get a signature on HWRS3. On desk: journal, calculator, HWRS, pencil, pen
4. Warm Up: Analyze the table on the next slide
Warm-up
X Y
-2 1
0 5
3 11
5 15
Is this a linear relationship? If so, find the slope, y-intercept, and write the equation. If not, explain why it is not linear.
Yes, this is a linear relationship.
As x goes up by 1, y goes up by 2.
m = 2b = 5
y = 2x +5
Mightyy = 49 + x or y = x + 49
b = $49 initial feem = $1 cost per shirt
No-Shrinky = 4.5 x or y = 4.5x + 0
b = $0 initial feem = $4.50 cost per shirt
Mightyy = 49 + x or y = x + 49
x = 20
y = 49 + 20 = $69
No-Shrinky = 4.5 x or y = 4.5x + 0
x = 20
y = 4.5 x 20 = $90
Mightyy = 49 + x or y = x + 49
y = 120
120 = 49 + x120 – 49 = x x = 71 t-shirts
No-Shrinky = 4.5 x or y = 4.5x + 0
y = 120
120 = 4.5x 120/4.5 = x
x is about 26 t-shirts
Week (x) 0 5 10 15 14MightyCost (y)
$49 $54 $59 $64 $63
No- ShrinkCost (y)
$0 $22.50 $45 $67.50
$63
What is the vocabulary word for when the costs are equal?
The break-even point or the point of intersection!
If I need to buy more than 14 shirts, Mighty is the better deal. If I need to buy less than 14 shirts, No-Shrink is the better deal.
Make a Table!
It is a linear relationship because each company is charging the same rate per t-shirt. Mighty charges $1 per shirt and No-Shrink charges $4.50 per shirt.
Mighty Tee: as n increases by 1, the cost increases by $1No-Shrink Tee: as n increases by 1, the cost increases by $4.50
The cost per T-shirt for this company is $2.50.The down payment , for no shirts, is $34.This cost is less per T-shirt than No-Shrink, but greater than Mighty.
Yes, it is a linear relationship!As the number of t-shirts increases by 1, the cost increases by $2.50.
Yes, (20, 84) lies on this graph.If you extend the table to n = 20, then C = $84.Or you can substitute the x and y into the equation!
The 20 means that if you buy 20 T-shirts it will cost $84.You can substitute the coordinates into the equation to make a true statement.