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
answer as best as you can in full sentence

answer: >

step-by-step explanation:

i've never seen the terminology 'slope-intercept' form before, but it seems fairly self-explanatory that it means 'of the form y = m + c'.

hence it is a simply rearrangement of the equation to start with, in order to make   the subject:

this is the graph in 'slope-intercept' form. from here it is easy to see that gradient   = and that y-intercept = 490.

the easiest way to draw a straight-line graph, such as this one, is to plot the y-intercept, in this case (0, 490), then plot another point either side of it at a fair distance (for example substitute   = -5 and   = 5 to procure two more sets of co-ordinates). these can be joined up with a straight line to form a section of the graph, which would otherwise extend infinitely either side - use the specified range in the question for x-values, and do not exceed it (clearly here the limit of -values is 0 ≤ x ≤ 735, since neither x nor y can be negative within the context of the question - the upper limit was found by substituting   = 0).

in function notation, the graph is:

the graph of this function represents how the value of the function varies as the value of x varies. looking back at the question context, this graph specifically represents how many wraps could have been sold at each number of sandwich sales, in order to maintain the same profit of $1470.

when the profit is higher, the gradient is not changed (this is defined by the relationship between the $2 and $3 prices, not the overall profit) - instead the -intercept is higher:

therefore we have gleaned that the new y-intercept is 531.

clearly i cannot see the third straight line. however the method for finding the equation of a straight line graph is fairly simple:

1. select two points on the line and write down their coordinates

2. the gradient of the line =

3. find the change in   (δ

4. find the change in   (δ

5. divide the result of stage 3 by the result of stage 4

6. this is your gradient

7. take one of your sets of coordinates, and arrange them in the form , where your   is the gradient you just calculated

8. there is only one variable left, which is   (the y-intercept). simply solve for this

9. now generalise the equation, in the form , by inputting your gradient and y-intercept whilst leaving the coordinates as   and

for example if the two points were (1, 9) and (4, 6):

δ = 6 - 9 = -3

δ = 4 - 1 = 3

=   = -1

i choose the point (4, 6)

6 = (-1 * 4) + c

6 = c - 4

c = 10

therefore, generally,

within the context of the question, i imagine the prices of the two lunch specials will be the same in the third month and hence the gradient will still be   - this means steps 1-6 can be omitted. furthermore if the axes are clearly labelled, you may even be able to just read off the y-intercept and hence dispose with steps 1-8!

i hope this you

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3