Linear Modelling

With Mitchy Moo and Big Aids

Joseph hires a math tutor to help him operate his CAS. The tutor charges him $20, plus an additional $10 per hour.

a) Construct a rule for the cost of the tutor

b) Construct a graph for the cost of the tutor versus the additional rate per hour.

c) If Joseph hires his math tutor for 3 and a half hours during the week, how much

does he owe?

a) Construct a rule for the cost of the tutor.Let n = number of hoursLet C = the cost of the tutorFind the fixed cost and additional charge per hourFixed cost = $20Additional charge = $10 per hour∴ C = 10n + 20

b) Construct a graph for the cost of the tutor versus the additional rate per hour.State the rule for a straight liney=mx+cSubstitute in for the equation found in part a) C=10n+20Write down the values for m and c m = 10, c = 20∴ the gradient = 10, and the y intercept = 20

c) If Joseph hires his math tutor for 3 and a half hours during the week, how much does he owe?C = 10n + 20

Substitute in the number of hours for nC=10(3.5) + 20C = 35 + 20C = 55∴ the cost for three and a half hours of tutoring is $55