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.
2x + 3y = 1200
2x-1200=-3y
1/3*(2x-1200)=1/3*-3y
2/3x-400=-y
-2/3x+400=y
The slope would be -2/3 and the y would be 400.
2. Describe how you would graph this line using the slope-intercept method. Be sure to write in complete sentences.
I would put a dot on (0,400) then I would use the slope to do the rest or go 2 points to the right and 3 to the down. After this it should look like 3,398.
3. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
F(x) = 2x + 1200
The function represents the x and y coordinates of a graph.
4. Graph the function using one of the following two options below. One 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.
2x + 3y = 1500
-3y = 2x – 1500
1/3* -3y = (2x – 1500)*1/3
-2/3x + 500 = y
This shows that the profits from the second month is greater than the profit of the first month because y equaled 400 in month 1 and equaled 500 in month 2.
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.
F(x)=mx + b
F(x) = mx + 300
F(x) = 6/9x + 300
F(x) = 2/3x + 300