Question

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.

Answer 1

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.

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

Hi, Gabe,
I'm sure plenty of people on OpenStudy.com would be glad to help you out. But could you help us first, by specifying where you need help? You've provided a graph; what were you hoping to achieve or gain by sharing this graph? Even if you just wanted someone's "OK" regarding the graph, it'd be better for you to say so specifically.
Good luck. Hope to hear back from you.

Answer 3

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 below:
1200=2x+3y
0=2x+3y-1200
-3y=2x-1200
divide everything by (-3)
y=(-2/3)x+400
m (slope)= -2/3
b (y intercept)= 400

This what I did for the first question. Now I need help graphing.

Answer 4

Thanks, Gabe. It really does help me considerably when you say here that you just need help with the graphing. I've checked your slope and y-intercept and find that they are perfect.

If the y-intercept is 400, we could re-write that as a point: (0,400).
Set up coordinate axes (x- and y-axes) so that you can easily plot (0,400). In your shoes, I'd make 400 the largest y value. What about the largest x value? If we let y=0, we'll be positioned on the x-axis. Go back to the original equation and let y=0; solve the result for x. That'll be your largest x value. OK?

Answer 5

Now, Gabe, I'm assuming that you've set up the coordinate axes and have plotted the y-intercept, which is the point (0,400). We know your slope is -2/3. Starting at (0,400), you could move 30 (or 300) units in the positive x direction, and then, 20 (or 200) units in the negative y-direction. In other words, your "run" would be 30 and your "rise" (which here is actually a drop) would be 20. You'll then have a new point. Draw a straight line through this point and the y-intercept (0,400).

Let me know whether or not this is clear for you; if it's not, what do you need to know?

Answer 6

I think so

Answer 7

@Luigi0210

Answer 8

@jim_thompson5910

Answer 9

Gabe, have you been able to graph this line and feel confident about the results? If not, what kind of help do you believe you need?

Answer 10

Can you put it in steps while showing the numbers and etc.

Answer 11

First, Gabe, which of my earlier suggestions have you been able to follow?
Have you set up coordinate axes (x- and y-axes) with appropriate scale divisions (0 to 400 on the vertical axis and 0 to 300 on the horizontal axis)?
Have you graphed the y-intercept, which is the point (0,400)?