Please help me with this assignment. I can't find any concrete help anywhere and I'm losing my hope.

Question

It's called ''Graphing Systems of Equation Writing Assignment''

The tasks are:

''Drive-In movie theatres are outdoor movie venues where people park facing a large screen and watch a movie from their own car. Daisy’s Drive-In charges $14.00 for a vehicle and an additional $4.00 per person in the car. Donald’s Drive-In charges $26.00 for a vehicle and an additional $2.00 per person in the car.''

I already know that the formula is 14.00 +4x = y for Daisy's drive in, and 26.00 +2x = y is for Donald's Drive in.

Now I need help with graphing it. ''Label x and y axis and give the graph a title. Label each line''

The last 2 tasks are ''What is the point of intersection on your graph? what does this mean in the context of the problem?''

and

''Compare the contrast of the theater options. When will daisy's be a better deal? When will Donald's be a better deal? explain how you know.''

I genuinely have no idea how to answer these, and on the top of that, English is not my first language and I don't know how to express myself properly especially in the last 2 questions. Please help me.

Answer 1

Answer 2

'What is the point of intersection on your graph? what does this mean in the context of the problem?''

The point of intersection is (6,38) or x=6, y=38

To find it, you need to take the two equations you wrote and equate them to each other

14 + 4x = 26 + 2x (answer x = 6)

and solve for x, then substitute the value of x into one of the equations to find y

y = 26 + 2*6 = 38

In the context of the problem it means that a family of 6 (x = 6) will pay the same amount of money, namely $38 (y=38) whether at Daisy’s or at Donald’s. So money is no issue here, and they should pick the venue based on other factors.

''Compare the contrast of the theater options. When will daisy's be a better deal? When will Donald's be a better deal? explain how you know.''

Daisy’s is better for small families (smaller than 6), because

14 + 4x < 26 + 2x for x < 6

(for example, a family of 5 would pay $34 at Daisy’s and $36 at Donald’s)

Donald’s is a better deal for large families (larger than 6)

14 + 4x > 26 + 2x for x > 6

(for example, a family of 10 would pay $54 at Daisy’s and $46 at Donald’s)

Answer 3

graphically they were two upward sloping straight lines

the smaller sloping line has a y intercept of 26

the larger sloping line has a y intercept of 14

set the y equations equal

4x +14 = 2x +26

2x =12

x =6 people in the car

y= 4(6)+14 = $38 = cost of either Donald or Daisey's Drive-In when there are 6 people in the car

y=2(6)+26 = $38 too.

Daisy is cheaper with 5 or less people in the car. She charges $34 for 5. Donald charges $36 for 5

Donald is cheaper with 7 or more people in the car. He charges $40 for 7, She charges $42 for 7

(although this doesn't cost the "social cost" of crowding too many people into one car. 6 people is already at or over the limit for some cars)

or use substitution and elimination

2 equations 2 unknown have a unique solution, if they are not linearly dependent (the same line) or contradictory (parallel lines)

y=4x+14

y =2x +26

double the 2nd equation and subtract the 1st equation from the result

2y=4x +52

y = 4x +14

y =38 dollar

plug into either equation to solve for x

38=2x+26

x = (38-26)/2 =12/2 =6 people in the car

or use matrix or linear algebra to solve for x and y

y=4x +14

4x-y = -14

y=2x +26

2x-y =-26

|4 -1| -14|

|2 -1| -26|

use row operations to get

| 1 0| 6|

| 0 1|38|

or use a graphing calculator to find the point of intersection (x,y) = (6,38)

or just carefully graph it yourself

title the horizontal axis x

title the vertical axis y

put some relevant title on top of the graph such as D&D's Drive-ins' Costs

maybe write Daisy at the top right of her line

and Donald on top right of his line

or just write 2x+26 above right of Daisy's line

and just 4x+14 at above right of Donald's line