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

Answer:

Given:

Profit of every sandwich = $2

Profit of every wrap = $3

x = sandwich

y = wrap

Last month:  2x + 3y = 1,470

Next month: 2x + 3y = 1,593

Based on the given equation:

Both still have the same profit. $2 for sandwiches and $3 for wraps.

The only reason why there is a difference in the total amount is the change in the number of sandwich or wrap sold in a given month.

Since, next month's total sale is higher than last month's total sale, it is safe to assume that the sale of sandwich or wrap is higher than last month's sale.

The graph of the functions for the two moths are similar because both conditions have same slope and they are different because they have different [tex]y-[/tex] intercept.

What is slope intercept form?

The graph of the linear equation   is a line with [tex]m[/tex] as slope, [tex]m[/tex] and [tex]b[/tex]   as the [tex]y-[/tex] intercept. This form of the linear equation is called the slope-intercept form, and the values of [tex]m[/tex] and [tex]b[/tex] are real numbers.

It is given that, the profit amount is [tex]$\$2$[/tex] for each sandwich and [tex]$\$3$[/tex] for each wrap and total profit is [tex]$\$1593$[/tex].

So, the equation is,

[tex]2x+3y=1593[/tex]

Change the equation in slope intercept form [tex]y=mx+b[/tex]

So,

[tex]2x+3y=1593[/tex]

Subtract [tex]2x[/tex] in both sides.

[tex]2x+3y-2x=1593-2x[/tex]

[tex]3y=1593-2x[/tex]

Divide each side by [tex]3[/tex].

[tex]$\frac{3y}{3}=\frac{1593}{3} -\frac{2x}{3}[/tex]

[tex]$\therefore y=-\frac{2x}{3}+531$[/tex]

So, the equation is,

[tex]y=-\frac{2x}{3}+531$[/tex]

The graph of the equation is shown below.

From the below graph, we will have two step down and three step right.

So, slope looks like rise over run.

So, the graphs represents, how many wraps and sandwiches were sold.

Both will have same slope, because if we will make the equation for this, it is like,

[tex]$2x+3y=1593$[/tex]

The calculation is follow for both condition is same.

Since, both conditions have same slope but different [tex]y-[/tex] intercept.

Hence, next month's total sale is greater than last month's total sale, it is safe to consider that the sale of sandwich or wrap is greater than last month's sale.

Learn more about slope intercept form here,

https://brainly.com/question/11824567

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