Warm-up! Mrs. B. is standing at (3,-3) and goes to throw an eraser to Hejaab, sitting at (-1,5). May, who sits at (0,1), suddenly stands up. Did Mrs. B. hit her with the eraser?! Did Mrs. B. hit her with the eraser?!

Linear Systems Point of Intersection

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 is 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? Years Owned Value ($) 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? Minutes UsedCell Phone Expenses Fido Telus The number of minutes when both plans cost the same amount

Tooba and Jesse decide that they are going to tutor other students in math to make some extra money. Some examples… Ex. 1: The Situation…

Jesse is helping Adam with math, using action figures and blocks to help him stay 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… she obviously needs some help! Oooooo…..? Yes, Ridhima, those are p-l-a-n-t-s.

Jesse charges $100 for the entire semester, and will help another student as much as needed. Tooba charges a flat amount of $20 for agreeing to tutor a student, then an additional $10 for each hour.

1. Write equations to represent these relationships, using ‘c’ for the cost of tutoring and ‘n’ for the number of hours. ToobaJesse c = 10n + 20c = 100

2. Graph both relationships on one grid. # of hours Cost ($) Cost vs. Number of Hours Jesse c = 100 Tooba c = 10n + 20

3. What is the point of intersection? # of hours Cost ($) Cost vs. Number of Hours (8,100) JesseTooba

4. What is the meaning of this p.o.i.? # of hours Cost ($) Cost vs. Number of Hours At 8 hours of tutoring, Jesse and Tooba both charge the same amount, $100. JesseTooba

5. Who would you recommend as a tutor? # of hours Cost ($) Cost vs. Number of Hours 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. JesseTooba

Mrs. Baumgartner’s class wants to raise money to go on a class trip. They’re flying to Greece to see the birthplace of Pythagoras. Another example… Ex. 2: The Situation…

Humor Break!

The students in Mrs. B.’s class decide to sell math magnets, such as the one below, knowing they will be hot sellers at SLSS.  

The supplies to make the magnets cost $2 per magnet, plus a one time cost of $10 for a glue gun. Students decide to sell the magnets for $4 each.   1. Write equations for the cost and revenue of the magnets, using ‘d’ for dollars and ‘m’ for the number of magnets. RevenueCost d = 4m d = 2m + 10

  2. Graph the relations to determine 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 Money ($) Cost d = 2m + 10 Revenue d = 4m They have to sell 5 magnets to break even and cover the $20 of cost.