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.

1.)change the equation to slope-intercept form. identify the slope and y-intercept of the equation. be sure to show all your work.

2.) describe how you would graph this line using the slope-intercept method. be sure to write using complete sentences.

3.)write the equation in function notation. explain what the graph of the function represents. be sure to use complete sentences.

4.) graph the function. on the graph, make sure to label the intercepts.

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.

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.

1. 2x + 3y = 1470
    3y = -2x + 1470
    y = -2/3x + 490 <== slope intercept form

2. y = -2/3x + 490slope = -2/3y int = (0,490)
    to graph, start at (0,490)since the slope is -2/3, we will go down 2       spaces, then to the right 3 spaces, then down 2 spaces, and to the right 3 spaces. It helps to find the x int which can be found by subbing in 0 for y into the equation and finding x. So ur x int is (735,0)...this is where ur line should cross the x axis.

3. function notation : f(x) = -2/3x + 490...not sure how to explain the meaning...sorry

4. graph the functionit will be the same line as the graph I explained before...y = -2/3x + 490
y int = (0,490)
x int = (735,0)

5. original :                            new :
    2x + 3y = 1470                 2x + 3y = 1593
    3y = -2x + 1470                3y = -2x + 1593
     y = -2/3x + 490                y = -2/3x + 531

similarities : Both of these equations will have the same slope, which is -2/3. Both lines are descending. Both lines are parallel to each other.

differences : These lines will have different x and y intercepts
y = -2/3x + 490 : y int = (0,490), x int = (735,0)
y = -2/3x + 531 : y int = (0,531), x int = (796.5,0)

6. pick 2 points on the line(0,300) and (450,0)
find the slope using the slope formula : slope = (y2 - y1) / (x2 - x1)
(0,300)x1 = 0 and y1 = 300
(450,0)...x2 = 450 and y2 = 0
now we sub and find the slope
slope = (0 - 300) / (450 - 0) = -300/450 reduces to -2/3

now we use y = mx + b
slope(m) = -2/3
use either of ur points...(450,0)...x = 450 and y = 0
now sub and find b, the y int
0 = -2/3(450) + b
0 = - 300 + b
300 = b

so ur equation is : y = -2/3x + 300or  2x + 3y = 900

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