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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.
change the equation to slope-intercept form. identify the slope and y-intercept of the equation. be sure to show all your work.
describe how you would graph this line using the slope-intercept method. be sure to write using complete sentences.
write the equation in function notation. explain what the graph of the function represents. be sure to use complete sentences.
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.
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.

30 people weigh 160 pounds or more

i think the amount would be $140.62

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

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