The mathalot company makes and sells textbooks. they have one linear function thst represents the cost of producing textbooks and another linear function that models how much income they can get from those textbooks. describe the key features that would determine if these linear functions ever intercepted.

It's only possible for the two lines to intercept isif they have different slopes.

When two lines have the same slope they would be parallel and never intercept.

If the lines have different slopes, they would  eventually intercept.

Two lines only can intercept if they have different slopes, if they have the same slope, the lines are parallel and they never intercept.

So if the cost of producing a book is different than the price of selling the book, the lines will intercept at some point.

Where the equations can be:

lose = A*x + b

win = C*x + d

where x is the number of books, A and C are the slopes, b and d are constants. Those two lines only will intercept if A is bigger than C, the intercept will be for x different than zero only when b is different than d

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x