# 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)...

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?

ishpiro | Certified Educator

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 + 20is shown below.

d) If Ashlee charged \$55 to repair a DVD, it means M = 55. The horizontal line with the equation M = 55 crosses the graph of the relation at the point with the coordinates (1.5, 55). This means it took Ashlee 1.5 hours to repair the DVD. This could be checked algebraically by plugging in h = 1.5:

25 + 20*1.5 = 55. For

For h = 1.5, M = 55.

e) If it took Ashlee 4.5 hours to repair a DVD player, then h = 4.5. The vertical line with the equation h = 1.5 will cross the graph of the relation at the point with the coordinates (4.5, 115). Ashlee would charge \$115 to repair this DVD:

for h = 4.5, = 25 + 20*4.5 = 115.

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.