Name _________________________________ 2.3 Graph Equations of Lines Write your questions and thoughts here!
Lesson goals – to graph linear equations in slope‐intercept form To graph linear equations in standard form Slope‐ intercept form – y‐intercept – To use slope‐intercept to graph an equation y
10
Graph y = x – 2. –10
x
10
x
–10
You Try – Graph y = 2x + 1. y
10
–10
–10
Standard form – 10
x‐intercept – 1 2.3 Graph Equations of Lines To use standard form to graph an equation Graph 2x + 3y = 12. 2 y
10
–10
10
x
10
x
–10
y
10
You Try – Graph 5x – 2y = 10. –10
–10
Using slope‐intercept form and standard form to graph linear equations makes the work quick and easy. The one type of linear equation that cannot be graphed in slope‐intercept form is a vertical line since the slope is undefined. But all linear equations can be graphed in standard form. Vertical line – Horizontal line – y
10
Graph x = 2 and y = ‐4. –10
10
–10
x
2.3 Practice – Graph equations of Lines Pg. 93 #3‐19 M4, 21‐23, 26, 27‐43 M4, 51 Graph the equation. Compare the equation with the graph of y = x. 3. y = 3x 7. y = 2x ‐ 1 Graph the equation. ଵ
11. y = 2x + 6 15. f(x) = ‐ ‐ x – 1 19. f(x) = ‐1.5x + 2 ଶ
Error Analysis – Describe and correct the error in graphing the equation. 21. y = 2x + 3 22. y = 4x ‐ 2 23. . Find the x‐ and y‐intercepts of the line with the given equation. 26. 3x – 4y = ‐12 27. 2x – y = 10 Graph the equation. Label any intercepts. 31. x + 4y = 8 35. 5x – y = 3 Graph the equation using any method. 43. 6y = 3x + 6 51. y – 5.5x = 6 39. y = 1.5 2.3 Application For all exercises, equations and work must be shown in order to receive credit. 1. Ms. Allen allowed her son to purchase an $1100 computer on layaway. He made a $250 initial payment and will make weekly payments according to the equation y = 850 – 50x where y is the amount he owes and x is the number of weeks. a) What is the original amount he owes? b) What is his weekly payment? c) Graph the model. d) How long will it take Ms. Allen’s son to pay for the computer in full? 2. Student tickets at Ramstein High School basketball games cost $2.00 each. Adult tickets cost $4.00 each. The ticket sales at the first game of the season totaled $2700. The equation 2x + 4y = 2700 can be used to model this situation. a) Graph the model. b) Describe what the intercepts represent. c) Use the graph to determine three scenarios of student and adult ticket sales that satisfy the model. 3. Mr. Sutton and Mr. Bradley kayak 1800 yards down a river. They drift with the current partway at 30 yards per minute and paddle partway at 90 yards per minute. The trip is modeled by 30x + 90y = 1800 where x is drifting time and y is paddling time (both in minutes). a) Graph the model. Determine a reasonable domain and range. What do the intercepts represent? b) If they paddle for 5 minutes, what is the total trip time? c) If they paddle and drift equal amounts of time, what is the total trip time?