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.

See below

Step-by-step explanation:

1.To write an equation in slope intercept form you apply the formula

y=mx+c where m is the slope, c is the y-intercept

The equation given is;

2x+3y=1470---------------------re-write as;

y=mx+c

3y=-2x+1470--------------------divide each side by 3

y= -2/3 x +470

2. Using the slope intercept form, you can form a table for values of x and y

then plot the values or use a graph tool to plot the equation

For example, to draw the linear graph you can use two points; (0,490) and (735,0)

x y

0 490

735 0

From the attached graph, the slope is -2/3 and the y-intercept is 490

3.To write an equation in function notation, it will be

f(x)= -2/3x + 490

This means the function f(x) depends on x and is defined by multiplying x by -2/3 and adding the result to 490

4.

From the graph, the intercepts are (0,490) and (735,0)

5.Given the new equation as

2x+3y=1593

Then , find the gradient

3y=-2x+1593

y=-2/3x +531

Here notice that the two graphs are the similar because they have the same slope.However, they are different because the y intercept in the second graph is 531 while that in the first graph is 490.The x intercept in the first graph is 735, while the x-intercept in the second graph is 796.5.

Equation:  2*x + 3*y = 1470

1. Slope-intercept form: y = a*x + b,  where a is the slope and b is the y-intercept. Isolating y form the equation:

2*x + 3*y = 1470

3*y = 1470 - 2*x

y = (-2/3)*x + 1470/3

y = (-2/3)*x + 490

slope: (-2/3)

y-intercept: 490

2. First locate the y-intercept at (0, 490), then starting from this point, move 3 units to the right and then 2 units down, and draw this point, which is (3, 488). Finally, draw a line that pass through these 2 points

3. Function notation is the same as Slope-intercept form with y-variable replaced by f(x). For this case: f(x) = (-2/3)*x + 490. The graph of this function represent how many wrap lunch specials has to been sold to earn $1,470 in a month as a function of the number of sandwich lunch specials sold.

4. See figure attached.

5. The new equation is:  2*x + 3*y = 1593

In Slope-intercept form:

2*x + 3*y = 1593

3*y = 1593 - 2*x

y = (-2/3)*x + 1593/3

y = (-2/3)*x + 531

In comparison to the first case:

step-by-step explanation:

b

step-by-step explanation: