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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.

Given
Profit on every sandwich (x) is $2
Profit on every wrap (y) is $3
Profit last month is $1470
Profit next month is $1593

Find
A: put the equation for last month's profit in slope-intercept form; identify the slope and y-intercept
B: describe in complete sentences how to graph this equation
C: write the equation in function notation. Explain what the function represents.
D: Graph the function; label the intercepts.
E: Explain how the graphs of the functions for last month's profit and next month's profit are similar and different.
F: (graph not supplied) Explain how you would write the equation for the graph.

Solution
A: To put a standard form equation into slope-intercept form, solve for y. Do that by subtracting the x-term and dividing by the coefficient of y.
  2x +3y = 1470
  3y = -2x +1470 . . . . subtract the x-term
  y = (-2/3)x + 490
    slope = -2/3
    y-intercept = 490

B: Graph this function by plotting the y-intercept on the y-axis. That point is (0, 490). Then find another point that is 2 units down for every 3 units to the right. Draw a line through that point and the y-intercept. (One such point is the x-intercept, (735, 0).)

C: The equation of part B can be written in function notation by replacing "y" with "f(x)".
  f(x) = (-2/3)x + 490
The function represents the number of wraps that must be sold in order to have a profit of $1470 as a function of the number of sandwiches sold.

D: See the attached graph.

E: The graph of the function for next month's profit is a line parallel to the one for the last month's profit. The slopes of the two graphs are the same. The intercepts of the two graphs are different.

F: You can write the equation using the slope-intercept form, provided that the y-intercept is given or can be read from the graph. Likewise, if the x-intercept is given, you can write the equation using that:
  y = (-2/3)(x - 'x-intercept')
Otherwise, you would have to determine a couple of points on the graph and use the 2-point form of the equation for a line to write the equation. For points (x1, y1) and (x2, y2), that form is
  y -y1 = (y2 -y1)/(x2 -x1)·(x -x1)

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