Ashlee repairs DVD players. She charges $25 To inspect the problem and $20/h to repair the device. a) write an equation to model this relation. b) Make a table of values. c) Graph this relation....

Ashlee repairs DVD players. She charges $25 To inspect the problem and $20/h to repair the device.

a) write an equation to model this relation.

b) Make a table of values.

c) Graph this relation.

d) Using your graphed relation, how long did it take Ashlee to repair the DVD player if she charged $55?

e) Using your graphed relation how much should Ashlee charge if it takes her 4.5 hours to repair the DVD player?

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 a) Denote the number of hours it takes Ashlee to repair a DVD by h. Then, the amount of money M Ashlee would charge to repair a DVD, in dollars would be 

M = 25 + 20

($25 to inspect and $20 per hour to repair)

b) A sample table of values would be

h    M

1    45

2     65

3     85

4    105

c) The graph of M = 25 +...

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maryaem | Student

a) Ashlee starts every repair job with a $25 inspection fee, then adds her $20 hourly charge for the work done. This gives us an equation that looks like: 

`M = 25+20h` 

where M is the total amount of money made after the repair job, and h is the number of hours Ashlee worked. 

 

b) To make a table of values for this equation, we can simply plug numbers in as values of h, and given those values, solve the equation for M

Let's say Ashlee worked one hour on a repair job. We can replace h in the equation with the number 1, then simplify to solve for M. 

 

`M=25+20(1)`

`M=45`

We can use these numbers, h=1 and M=45 to start our table of values, then continue using the same method with different values of h.

h   M

1   45

2   65

3   85

4   105

5   125

 

c) To graph this relation, we can use our values as our x-axis, and our M values as our y-axis. Simply plot any two points from your table of values - let's say (1, 45) and (3, 85), connect the dots and extend the line. This works in this case because our equation is linear. 

 

d) For a job where Ashlee earns $55, M=55. Since M values make up the y-axis on our graph, we can look at the graph above to see where the plotted line intersects y=55. In this case, where y=55, x=1.5. Our h value is 1.5, which means Ashlee worked for 1.5 hours on this particular repair. 

e) We can use a similar method to find the M value on our graph, given the h value as 4.5 hours. Find where the graphed line intersects x=4.5, and you will find that at that point, y=115. This gives us M=115, so Ashlee should charge $115 for this repair job.