Section 3 3 Partial Variation Partial variation The

Section 3. 3 – Partial Variation Partial variation: The line in this graph will NOT start at or pass through y=0, or b≠ 0 Ex: y=8 x+3, The cost of a rental car is $200 a day plus $0. 5 per km driven The formula for the line is: y = 8 x + 3 Slope = m = 8 Y-intercept = Constant = +3

Colton repairs heating and air-conditioning systems. When he is out on a service call, he charges a service call fee of $75 plus $65 per hour for his labour. a) What are the initial value and the rate of change? Initial Value = Rate of Change = $75 $65 b) Create a table of values for the cost of 0 h to 5 h of Colton’s services. How does your table show the initial value and the rate of change? Hours 0 1 2 3 4 5 Total 75 140 205 270 335 400 c) Predict what a graph of the table of values would look like. Slope: 65 y-intercept: 75 No line, Solid Line or Dashed Line d) What does Colton charge for a job that takes 1. 5 h? Show your work. 65 (1. 5) + 75 = $172. 50 e) How many hours would Colton have to work to earn $855? 65 x + 75 = 855 65 x = 855 -75 65 x = 780 / 65 x = 12 hours

Taneeka borrowed $400 from her parents to help pay for a driver training course. She agrees to pay her parents back at a rate of $50 at the end of each week. Taneeka is keeping track of how much she owes her parents on a weekly basis. a) What are the initial value and the rate of change? initial value = 400 rate of change = -50 b) Write an equation for the relationship. y = -50 x + 400 c) Use the equation to determine how long it will take Taneeka to pay off her parents. 0 = -50 x + 400 0 – 400 = -50 x -400 / -50 = x 8=x

d) Create a scatter plot of the data. e) Decide whether to draw a line, dashed or solid, through the points. Explain your decision. f) How does your graph show the initial value and the rate of change? - no line drawn because there are no values between the plotted points. g) How do you know that the graph represents a partial variation relationship? - the line does not intercept the graph at (0, 0)