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 yintercept of the equation. Be sure to show all of your work.
2x+3y=1200
3/3y=-2x/3 +1200/3
Y=- 2/3x+400
The slope is -2/3 and the y intercept is 400.
2. Describe how you would graph this line using the slope-intercept method. Be
sure to write in complete sentences.
To graph this equation, 400 would be the intercept on the y-axis. The rise over run
is – 2/3, so I would move down two units and over three. I would repeat this until
the line crossed over the x-axis.
3. Write the equation in function notation. Explain what the graph of the function
represents. Be sure to use complete sentences.
X
f(x)=- 2/3x + 400
y
25 f(25)=- 2/3(25)+400 383.3
100 f(100)=- 2/3(100)+400
333.3
200 f(200)=- 2/3(200)+400
266.7
300 f(300)=- 2/3(300)+400
200.0
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.
Expanding:
Reorder the terms:
f(x) = 400 + -0.66x
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
Y=- 2/3x + 500
If the next month’s profit increased to 1500, the profit for each individual phone
and tablet case would remain the same. Tablet cases would result in a3 dollar
profit, while phone cases earn 2 dollars. The graph is representing the overall
profit in relation to the number of items sold. The slope of the new graph would
remain the same at 2/3. The only difference would be the y intercept moving 400
to 500.
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.
The new equation for the 3rd ( ) is y = - 2/3x + 300. The slope would remain the
same because the profit for individual cases sold has not changed, leaving slope at
– 2/3. I determined this by finding the rise and run of the graph to be the same.
The y intercept was 300, meaning this is the only portion of the equation to be
altered.