The annual cost of owning and operating a car, C dollars, is a linear function of the distance, d kilometers, it is driven c = md + b
The cost is $4600 for 10 000 km and $9100 for 25 000 km.
(a) Determine the values of m and b.
(b) Write c as a function of d. Choose the correct choice from the following options.
A) m = 0.3 and b = 1500	B) m = 0.3 and b = 1600	C) m = 0.3 and b = 1700	D) m = 0.3 and b = 1800	E) None
Solution:   (a)   c = md + b   The cost is $ 4600 for 10 000 km   4600 = m (10 000) + b   10 000 m + b = 4600   b = -10 000 m + 4600 ------- (i)   The cost is $ 9100 for 25 000 km   9100 = m (25 000) + b   9100 = 25 000 m + b   25 000 m + b = 9100   b = -25 000 m + 9100 --------- (ii)   From equation (i) and (ii) we get;   -10 000 m + 4600 = -25 000 m + 9100   -10 000 m + 25 000 m = 9100 – 4600   15 000 m = 4500   m = 4500/15 000   m = 3/10= 
<gadget id="calculator">3/10</gadget>
<output>3/10 = around 0.3</output>
0.3   Now, put the value of m= 0.3 in equation (i) we get;   b = -10 000 (0.3) + 4600   b = -3000 + 4600= 
<gadget id="calculator">-3000 + 4600</gadget>
<output>1_600</output>
1600   Answer: m= 0.3 and b = 1600   (b) c = md + b   m = 0.3   b = 1600   c = 0.3d + 1600   Answer: c = 0.3d + 1600   Answer m = 0.3 and b = 1600
<result>B</result>
The annual cost of owning and operating a car, C dollars, is a linear function of the distance, d kilometers, it is driven c = md + b
The cost is $4600 for 10 000 km and $9100 for 25 000 km.
(a) Determine the values of m and b.
(b) Write c as a function of d.