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.
Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.

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

Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.

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.

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.

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 1

2x + 3y = 1470
3y = -2x + 1470
y = -2/3x + 490 <== slope intercept form
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to graph :
the slope = -2/3....the y int = (0,490)
start at (0,490), and since the slope is -2/3, go down 2 spaces, then to the right 3, plot those points, then down 2, and to the right 3, plot those points...keep doing this, and when done, connect the dots.
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function notation : f(x) = -2/3x + 409
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2x + 3y = 1593               2x + 3y = 1470
3y = -2x + 1593              3y = -2x + 1470
y = -2/3x + 531               y = -2/3x + 490

similarities : They both have a slope of -2/3
differences : They both have different x intercepts and different y intercepts
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the graph :
(0,300)(450,0)
slope = (0 - 300) / (450 - 0) = -300/450 = - 2/3

y = mx + b
slope(m) = -2/3
(0,300)...x = 0 and y = 300
sub and find b, the y int
300 = -2/3(0) + b
300 = b

so this equation is : y = -2/3x + 300