Graphing Systems of Equations Writing Assignment

Question

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.

1. Graph the system of equations. Label the x and y axis and give the graph a title. Label each line. 

Answer 1

for Daisy: y = 4x + 14

Graphically, it's a straight line with slope =4 and y intercept = 14, x intercept = -7/2 = -3.5

plot the two points (0,14) and (-3.5, 0) connect them with a straight line

for Donald's dive-in: y = 2x + 26, the line has slope = 2, y intercept = 26 and x intercept = -13

plot those two intercept points (0,26 and (-13, 0) connect them with a straight line

the two lines intersect when

4x+14 = 2x +26

2x = 12

x = 6

y = 38

the point (6, 38)

best way to draw the lines is plot the y intercept of each line and connect it to the point (6,38)

label the lines y=4x+14 and y=2x+26

or y and y'

or maybe f(x) and g(x)

or f(x) = 4x+14 and g(x) = 2x+26

or

maybe just 4x+14 and 2x +26

or label the lines by letters such as Da and Do to indicate which is

Daisy and which is Donald's drive in

then you want a title. Maybe "Drive-in Costs"

maybe label the y axis as C or $ or just y

and the x-axis maybe P for person or just x

or follow whatever pattern and symbols the instructor or text uses

while the two lines cover all real numbers, what you really should graph is just the integer points for the x or P coordinates, as the persons in the vehicles are only whole numbers, not fractions. Also you only want points in quadrant I, as the lines in quadrant II and III involve negative numbers of persons.

One way to indicate you only want integer values of x is plot the points with integer x coordinates, and connect them with a dotted line. or if you use a full line, make the integer points darker or larger, so they stand out.

the only realistic graph of the problem is plot about 6 points for each line

for y=4x +14,

(1,18), (2,22), (3,26), (4, 30) (5,34) (6,38)

for y= 2x +26

(1, 28), (2,30), (3, 32), (4,34), (5, 36), (6, 38)

the last point (6,38) is the same for each line.

. Odds are for most vehicles, about 6 persons is the maximum number'

With less than 6 persons per vehicle Daisy's Drive-in is cheaper

with more than 6 persons per vehicle, Dona'd's Drive-in is cheaper

for 6 in vehicle, the cost is the same.