Warm-up!Warm-up!

Mrs. B. is standing at (3,-3) and goes to throw an Mrs. B. is standing at (3,-3) and goes to throw an eraser to Hejaab, sitting at (-1,5). May, who sits eraser to Hejaab, sitting at (-1,5). May, who sits

at (0,1), suddenly stands up. at (0,1), suddenly stands up.

Did Mrs. B. hit her with the eraser?!Did Mrs. B. hit her with the eraser?!Did Mrs. B. hit her with the eraser?!Did Mrs. B. hit her with the eraser?!

Linear SystemsLinear SystemsPoint of Intersection Point of Intersection

What is a linear system?What is a linear system?

two or more equations (of linear relations) considered together

two or more equations (of linear relations) considered together

we will be finding and interpreting p.o.i.we will be finding and interpreting p.o.i.

to solve a linear system means to find the point of intersection (p.o.i.)to solve a linear system means to find the point of intersection (p.o.i.)

What What isis a point of intersection? a point of intersection?

the point where both lines have the same x and y values

the point where both lines have the same x and y values

the p.o.i is (-2, -1)

What does this p.o.i. mean?What does this p.o.i. mean?

Years Owned

Val

ue

($)

Mrs. B.’s car

Mr. B.’s car The number of years Mr. and Mrs. B. own their cars until they are both worth the same.

And this one?And this one?

Minutes Used

Cel

l P

ho

ne

Exp

ense

s

Fido

Telus

The number of minutes when both

plans cost the same amount

Tooba and Jesse decide Tooba and Jesse decide that they are going to tutor that they are going to tutor other students in math to other students in math to make some extra money.make some extra money.

Some examples…Some examples…Ex. 1: The Situation…Ex. 1: The Situation…

Jesse is helping Adam with math, using Jesse is helping Adam with math, using action figures and blocks to help him stay action figures and blocks to help him stay

interested.interested.

If you had 8 men, and I killed 2, you now have

6 men left.

I don’t get it…

Tooba is tutoring Ridhima…Tooba is tutoring Ridhima…

she obviously needs some help!she obviously needs some help!

Oooooo…..?Yes,

Ridhima, those are p-l-a-n-t-s.

Jesse charges $100 for the entire Jesse charges $100 for the entire semester, and will help another student semester, and will help another student

as much as needed.as much as needed.

Tooba charges a flat amount of $20 for Tooba charges a flat amount of $20 for agreeing to tutor a student, then an agreeing to tutor a student, then an

additional $10 for each hour.additional $10 for each hour.

1. Write equations to represent these 1. Write equations to represent these relationships, using ‘c’ for the cost of relationships, using ‘c’ for the cost of tutoring and ‘n’ for the number of hours.tutoring and ‘n’ for the number of hours.

ToobaToobaJesseJesse

c = 10n + 20c = 100

2. Graph both relationships on one grid.2. Graph both relationships on one grid.

# of hours

Cos

t ($

)

Cost vs. Number of Hours

1 2 3 4 5 6 7 8 9 10 11 12

102030405060708090

100110120 JesseJesse

c = 100

ToobaTooba

c = 10n + 20

3. What is the point of intersection?3. What is the point of intersection?

# of hours

Cos

t ($

)

Cost vs. Number of Hours

1 2 3 4 5 6 7 8 9 10 11 12

102030405060708090

100110120

(8,100)

JesseJesse ToobaTooba

4. What is the meaning of this p.o.i.?4. What is the meaning of this p.o.i.?

# of hours

Cos

t ($

)

Cost vs. Number of Hours

1 2 3 4 5 6 7 8 9 10 11 12

102030405060708090

100110120

At 8 hours of tutoring, Jesse

and Tooba both charge

the same amount, $100.

JesseJesse ToobaTooba

5. Who would you recommend as a tutor?5. Who would you recommend as a tutor?

# of hours

Cos

t ($

)

Cost vs. Number of Hours

1 2 3 4 5 6 7 8 9 10 11 12

102030405060708090

100110120

If a person needs exactly 8 hours of

tutoring, he/she can pick either person

(they cost the same).

If more than 8 hours is needed, Jesse is cheaper.

If less than 8 hours is needed, Tooba is cheaper.

JesseJesse ToobaTooba

Mrs. Baumgartner’s Mrs. Baumgartner’s class wants to raise class wants to raise

money to go on a class money to go on a class trip. They’re flying to trip. They’re flying to

Greece to see the Greece to see the birthplace of Pythagoras.birthplace of Pythagoras.

Another example…Another example…

Ex. 2: The Situation…Ex. 2: The Situation…

Humor Break!Humor Break!

The students in Mrs. B.’s class The students in Mrs. B.’s class decide to sell math magnets, such decide to sell math magnets, such as the one below, knowing they will as the one below, knowing they will

be hot sellers at SLSS.be hot sellers at SLSS.

The supplies to make the The supplies to make the magnets cost $2 per magnet, magnets cost $2 per magnet,

plus a one time cost of $10 for a plus a one time cost of $10 for a glue gun. Students decide to glue gun. Students decide to sell the magnets for $4 each.sell the magnets for $4 each.

1. Write equations for the cost and revenue of 1. Write equations for the cost and revenue of

the magnets, using ‘d’ for dollars and ‘m’ for the magnets, using ‘d’ for dollars and ‘m’ for the number of magnets.the number of magnets.

RevenueRevenueCostCost

d = 4md = 4md = 2m + 10d = 2m + 10

2. Graph the relations to determine 2. Graph the relations to determine when Mrs. B.’s class will break even.when Mrs. B.’s class will break even.

Break-even point:

the point on the graph where the costs = the revenue

there is no profit or no loss

Money vs. # of Magnets

# of magnets

Mon

ey (

$)

1 2 3 4 5 6 7 8 9 10 11 12

2468

1012141618202224

CostCost

d = 2m + 10

RevenueRevenue

d = 4m

They have to sell 5 They have to sell 5 magnets to break magnets to break

even and cover the even and cover the $20 of cost.$20 of cost.