Question

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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

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.

Slope =-2/3x
y intercept=400
2x + 3y = 1200

2x-1200=-3y

1/3*(2x-1200)=1/3*-3y

2/3x-400=-y

-2/3x+400=y

2.Describe how you would graph this line using the slope-intercept method. Be sure to write in complete sentences.

I would dot (0,400) then go 3 down and 2 right. 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


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.

The graph is same same because it has the same slope. It just has a different y intercept.

2x + 3y = 1500

-3y = 2x – 1500

1/3* -3y = (2x – 1500)*1/3

-2/3x + 500 = y

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 intercept is 300

F(x) = 6/9x + 300 6/9 is the slope

F(x) = 2/3x + 300 6/9 simplified is 2/3