1. Day 2: Solving Linear Systems by Graphing
Unit 2: Linear Systems
Did you know that unless food is mixed with saliva, you can’t taste it?

2. Learning Goals
To be able to find a solution to two linear relations by graphing

3. Graph each of the following lines using an appropriate method (table of values, intercepts, slope/y-intercept)
𝑦=−𝑥+4
𝑥−2𝑦=10

4. 𝑦=−𝑥+4 𝑚=−1 𝑦−intercept=(0, 4)
𝑥−2𝑦=10 0 −2𝑦=10 − 2𝑦 2 = 10 −2 𝑦=−5 𝑥−2 0 =10 𝑥=10

5. What are the coordinates of the point of intersection of these two lines?
(6, −2)
This ordered pair is called the solution to the linear system: it is the point that satisfies both equations.
It is also called the point of intersection (POI).

7. Stephanie wants to rent a car for a weekend trip
Stephanie wants to rent a car for a weekend trip. Kelly’s Kars charges $95 for the weekend plus $0.15/km. Rick’s Rentals charges $50 for the weekend plus $0.26/km. Which company charges less? Step 1: Write ‘Let…” statements Let 𝑥 represent the distance driven in km Let 𝑦 represent the total cost of the car rental in dollars

8. Stephanie wants to rent a car for a weekend trip
Stephanie wants to rent a car for a weekend trip. Kelly’s Kars charges $95 for the weekend plus $0.15/km. Rick’s Rentals charges $50 for the weekend plus $0.26/km. Which company charges less? Step 2: Write an equation for each option 𝑦=0.15𝑥+95 Kelly’s Kars 𝑦=0.26𝑥+50 Rick’s Rentals

9. Stephanie wants to rent a car for a weekend trip
Stephanie wants to rent a car for a weekend trip. Kelly’s Kars charges $95 for the weekend plus $0.15/km. Rick’s Rentals charges $50 for the weekend plus $0.26/km. Which company charges less? Step 3: Decide the easiest method to graph (table of values, intercepts, slope/y-intercept) Since both are in 𝑦=𝑚𝑥+𝑏 form, slope/y-intercept is easiest

10. Stephanie wants to rent a car for a weekend trip
Stephanie wants to rent a car for a weekend trip. Kelly’s Kars charges $95 for the weekend plus $0.15/km. Rick’s Rentals charges $50 for the weekend plus $0.26/km. Which company charges less? Step 4: Graph each line

11. Stephanie wants to rent a car for a weekend trip
Stephanie wants to rent a car for a weekend trip. Kelly’s Kars charges $95 for the weekend plus $0.15/km. Rick’s Rentals charges $50 for the weekend plus $0.26/km. Which company charges less? Step 5: Find the point of intersection (409, 156)

12. Stephanie wants to rent a car for a weekend trip
Stephanie wants to rent a car for a weekend trip. Kelly’s Kars charges $95 for the weekend plus $0.15/km. Rick’s Rentals charges $50 for the weekend plus $0.26/km. Which company charges less? Step 6: Give a concluding statement If Stephanie drives 409 km, both companies charge the same. If she drives less than 409 km, Rick’s Rentals charges less. If she drives more than 409 km, Kelly’s Kars charges less.

13. Graphing Calculators
Desmos app

14. Find the solution (or the POI) to the following two equations using graphing technology.
4𝑥+3𝑦=6 𝑦= 1 4 𝑥−3

15. Success Criteria
I CAN find the solution (or the point of intersection) for two linear equations by graphing by hand or using technology

16. To Do…
pg. 26 # 1, 2a, 3, 4, 5c, 6, 8, 9, 14a
Screenshot 3c) and post to #coolgraph
Extra help Tuesday after school, Thursday at lunch (rm 209)
Check the website daily for updates, missed notes, assignment solutions