Question

Please help with this (:

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.

Answer 1

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. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
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.

Answer 2

@PrincessHush

Answer 3

2x + 3y = 1470......slope intercept form is y = mx + b
3y = -2x + 1470
y = -2/3x + 1470/3
y = -2/3x + 490
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this line would be graphed by finding the x and y intercept.
y = -2/3x + 490
the y intercept when the equation is in y = mx + b form is in the m position. So the y intercept is (0,490).
the x intercept can be found by subbing in 0 for y
0 = -2/3x + 490
2/3x = 490
x = 490/(2/3)
x = 490 * 3/2
x = 735...so the x intercept is (735,0)

plot your points...and you will notice that if you start at the y axis....and your slope is -2/3...that means start at (0,490)....go down 2 spaces then to the right 3 spaces, then down 2, then to the right 3...you will cross the x axis at (735,0).
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to write in function notation....replace the y with f(x).
f(x) = -2/3x + 490
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you can do the graphing
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first month : y = -2/3x + 490
next month : 2x + 3y = 1593
3y = -2x + 1593
y = -2/3x + 1593/3
y = -2/3x + 531
well...the x and y intercepts are different...but the slopes are the same.
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take 2 points on your graph....(150,200) and (300,100)
use slope formula to find the slope
slope(m) = (y2 - y1) / (x2 - x1)
(150,200)....x1 = 150 and y1 = 200
(300,100)..x2 = 300 and y2 = 100
now sub
slope(m) = (100 - 200) / (300 - 150)
slope(m) = -100/150
slope(m) = - 2/3

now use y = mx + b
slope(m) = -2/3
using either of your points ...(100,200)...x = 100 and y = 200
now we sub
200 = -2/3(100) + b
200 = -200/3 + b
200 + 200/3 = b
600/3 + 200/3 = b
800/3 = b

so your equation is : y = -2/3x + 800/3

Answer 4

@texaschic101 ah okay I understand that (: Im just confused on which one goes with 1-6.

Answer 5

there in order

Answer 6

@texaschic101 thank you