Digits, Grade 7, Volume 1, Homework Helper

#### Part 1

Example Comparing Linear Equations

An 8th grade class wants to hire a DJ for their end-of-the-year party. table with 1 row and 3 columns , row1 column 1 ,

• a. Which DJ charges the highest hourly rate?

• b. Which equation(s) show a proportional relationship between the number of hours x and the total cost y?

• c. If you only have \$150 to spend, which DJ can you hire for the longest period of time?

Solution

• a. The slope of each equation represents the costs per hour.

table with 2 rows and 3 columns , row1 column 1 ,

DJ A charges \$20 per hour, DJ B charges \$40 per hour, and DJ C charges \$25 per hour. DJ B charges the most per hour.

• b. Equations of the form y = mx show a proportional relationship between x and y. Only the equation y = 40x shows a proportional relationship between the number of hours and the total cost.

• c. In each equation, y represents the total cost for x hours. You need to find the x-value that corresponds to a y-value of 150. Substitute 150 for y and solve for x.

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