Question

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. 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 1

Let
x--------> the number of sandwich lunch specials sold
y-------> the number of wrap lunch specials sold

we know that
2x+3y=1470

Part 1) Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.

we know that
the equation to slope-intercept form is of the form
y=mx+b
so
2x+3y=1470------> solve for y
3y=1470-2x-----> divide by 3 both sides
y=(-2/3)x+1470/3
y=(-2/3)x+490

the slope m=-2/3
the y-intercept is 490


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

the slope is -2/3  and the y-intercept is 490

Plot the point (0,490)------>  the y-intercept.
With the slope count 3 squares to the right and 2 squares down and plot that point, which is (0+3,490-2)--------> (3,488)
Draw a line through the two points  

Part 3) Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.

In function notation, the equation is:
f(x)=(-2/3)x+490
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.

Part 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

using a graph tool
see the attached figure

Part 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

we have that
2x+3y=1593
3y=1593-2x--------> y=(-2/3)x+531
slope=(-2/3)
y intercept=531
therefore
similarities : same slope
differences : y intercepts are different.
This is basically telling me that the lines are parallel lines because they have the same slope.

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

Select two points on the line and write down their coordinates

Let
 A( 0,300)  B (450,0)
a) find the slope
m=(y2-y1)/(x2-x1)----> m=(0-300)/(450-0)----> m=-2/3
b) with the slope m=(-2/3) and the point A (0,300)
y-y1=m*(x-x1)-----> y-300=(-2/3)*(x-0)----> y=(-2/3)x+300

the answer Part 6) is
y=(-2/3)x+300