Question

please help im confused

Answer 1

A company produces accessories for smart phones and tablets. The profit on each smart phone case is $2, and the profit on each tablet case is $3. The company made a profit of $1,200 on the cases last month. The equation 2x + 3y = 1,200 represents the company's profit from cases last month, where x is the number of smart phone cases sold and y is the number of tablet cases sold.
1. Change the equation into slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all of your work.
2. Describe how you would graph this line using the slope-intercept method. Be sure to write in complete sentences.
3. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
4. Graph the function using one of the following two options below. On the graph, make sure to label the intercepts.
• You may graph your equation by hand on a piece of paper and scan your work.
• You may graph your equation using graphic technology that can be found in the Course Information area.
5. Suppose in the next month, the total profit on smart phone cases and tablet cases is $1,500. The profit amounts are the same, $2 for smart phone case and $3 for the tablet case. In a paragraph of at least three sentences, explain how the graphs of the functions for the two months are the same and how they are different. Be sure to use complete sentences.
6. Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations.

Answer 2

to change the formula to slope intercept form you would change it to
y=mx+c
so if you make y the subject from the formula
2x +3y=1200 what would you get

Answer 3

im sorry im horrible at this kind of math

Answer 4

ok lets work through it together

Answer 5

ok

Answer 6

first you need to move your 2x to the left hand side and note that because it is originally +2x when you move it over the equal sign it become -2x

Answer 7

got it @catlovesyou

Answer 8

yea

Answer 9

ok then so the equation is now
3y=1200-2x

Answer 10

ok

Answer 11

you now need to eliminate the 3 on the LHS by dividing by 3 on both sides and your final equation is \[y=\frac{ 1200-2x }{ 3 }\]

Answer 12

but because we want it in the form y=mx+c
it would be\[y=\frac{ -2x+1200 }{ 3 }\]
got it @catlovesyou

Answer 13

yea

Answer 14

ok now in the form y=mx+c
we know m is your gradient which is also the slope
and c is the y intercept

Answer 15

so from our new equation if we split it into parts to make it simpler
\[y=\frac{ -2x }{ 3 }+\frac{ 1200 }{ 3 }\]

Answer 16

so thats number one right

Answer 17

yep

Answer 18

ok i get that

Answer 19

cool. so can you figure out what the slope intercept is
and the y-intercept

Answer 20

umm let me see

Answer 21

im confused

Answer 22

still

Answer 23

ok no problem
so we figured out our equation to be \[y=\frac{ -2x }{ 3}+ \frac{ 1200 }{ 3 }\]

Answer 24

yea

Answer 25

and we said m represents the slope in the form y=mx+c

which means the -2/3 would be your m

Answer 26

ok

Answer 27

so what would c be then?

Answer 28

400

Answer 29

cause 1200/3=400

Answer 30

yep.correct

Answer 31

ok

Answer 32

so Q1 is done...thumbs up

Answer 33

ok

Answer 34

so q2 i can say that -2/3 x would be the x intercept and 400 would be y intercept

Answer 35

yep

Answer 36

but you still need to find at least two points you would use to graph

Answer 37

ok how do i do that

Answer 38

as in when y=0 and when x=0
if you substitute those values into the equation you would have coordinates you can use for graphing

Answer 39

so lets try when x=0

Answer 40

ok

Answer 41

\[y=\frac{ -2\times0 }{ 3 }+\frac{ 1200 }{ 3 }\]

Answer 42

solve that and what would you get?

Answer 43

so it will be -2/3+1200/3

Answer 44

nope -2x0=0

Answer 45

o yea

Answer 46

so it would be 0/3 +1200/3

Answer 47

yea

Answer 48

which equal ???

Answer 49

400

Answer 50

0/3=0

Answer 51

1200/3=400

Answer 52

correct
now that is a cordinate when x=0 y=400
(0,4000

Answer 53

sorry (0,400)

Answer 54

got that??

Answer 55

yea

Answer 56

ok now try substitute y=0

Answer 57

ok

Answer 58

\[0=-2x/3+1200/3\]

Answer 59

\[0=-2/3+400\]

Answer 60

than you would divide 400 on both sides right

Answer 61

you were not supposed to eliminate the x

Answer 62

it should be

Answer 63

o ok \[0=-2/3x+1200/3\]
\[0=-2/3x+400\]