Could anybody give me some help? I'm a little confused .-. <3 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 from last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. ( Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences)

Accepted Solution

What your teacher wants is for you to isolate y in the given equation. In other words, get y all by itself. 

To do this, you'll do two basic steps:
Step 1) Subtract 2x from both sides
Step 2) Divide both sides by 3

Let's do that and we get...
2x+3y = 1470
2x+3y-2x = 1470-2x ... apply step 1
3y = 1470-2x
3y = -2x+1470
3y/3 = (-2x+1470)/3 ... apply step 2 
y = (-2x)/3 + 1470/3
y = (-2/3)x + 490

After isolating y, we get y = (-2/3)x + 490
To get this into function notation, we simply replace y with f(x) to get the final answer f(x) = (-2/3)x+490 which is the same as writing [tex]f(x) = -\frac{2}{3}x+490[/tex]

This graph represents all of the ordered pairs (x,y) that make the original equation true. For example, the point (x,y) = (0,490) is on the line where x = 0 and y = 490. This point is when 0 sandwiches are sold and 490 wraps are sold yielding a profit of $1470. Another point on this line is (x,y) = (3,488). Now 3 sandwiches have been sold along with 488 wraps leading to the same profit of $1470. Any ordered pair point you pick on the line should lead you to the same profit.