Question

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Part 1.Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Part 2. Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Part 3. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Part 4. Graph the function. 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 or you may use graphing technology.
Part 5. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.

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Answer 1

1.   y = -⅔x + 490    

2.   I would start with the y-intercept(490) on the graph. Then from that point, I would use rise/run to find the next point: I would go down two points (because the slope is negative), and run three points to the right.

3.   f(x) = -⅔ + 490. The graph represents the total profits of last month.

4.   View file below.

5.   The graphs of these functions are similar in the fact that they are parallel to each other, therefore having the same slope.Both lines are also negative. They are different in that they do not have the same y-intercept or x-intercept.