Chapter 9.5, Problem 27IP

a.

To determine

To write an equation representing $\text{y}$ the total cost of having a photo taken and $\text{x}$ the number of $5\times 7\text{s}$ got from the studio.

Answer to Problem 27IP

Total cost at lifetime photos is $\text{y}=15\text{x}+18$ and at Family photos is $\text{y}=15\text{x}+12$ .

Explanation of Solution

Given information:

The given statement is:

“The table shows the cost of the sitting fee and each $5\times 7$ portrait at two photography studios.”

  

The equation to represent the total cost at Lifetime photos is:

  $\text{y}=15\text{x}+18$

The equation to represent the total cost at Family photos is:

  $\text{y}=15\text{x}+12$

b.

To determine

To graph the equations on the same plane.

Explanation of Solution

Given information:

Total cost at lifetime photos is $\text{y}=15\text{x}+18$ and at Family photos is $\text{y}=15\text{x}+12$ .

Graph:

The graph for both the equations is given below:

c.

To determine

To explain whether the lines will intersect or not.

Answer to Problem 27IP

No, the lines will never intersect.

Explanation of Solution

Given information:

The graph for the equations representing the cost of two studios are:

The lines will never intersect, because they have the same slope $15$ .

d.

To determine

To compare the slopes of each line.

Answer to Problem 27IP

Both the lines have the same slope.

Explanation of Solution

Given information:

The equations of the lines are $\text{y}=15\text{x}+18$ and $\text{y}=15\text{x}+12$ .

The slopes of both the lines are $15$ .

Hence, both the lines have the same slope.