initial value, rate of change, rise, run, slope, y-intercept
TEKS 7(1)(A), 7(7)
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?
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.