Algebra 1

Question

The linear function f(x) = 0.2x + 79 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents the average test score in your science class, where x is the number of the test taken.
 

x	g(x)
1	86
2	84
3	82

Part A: Determine the test average for your math class after completing test 2. (2 points)

Part B: Determine the test average for your science class after completing test 2. (2 points)

Part C: Which class had a higher average after completing test 4? Show work to support your answer. (6 points)

Answer 1

Average of math class after taking test 2, f(2) = 0.2 * (2) + 79 = 79.4

Average of science class after taking test 2, g(2) = 84,  (as shown in the table)

Average of math class after taking test 4, f(4) = 0.2 * (4) +79 =79.8

Average of science class after taking test 4, g(4) = 80  (Explanation below)

so, f(4) < g(4)

Explanation:

the table follows a straight line, y- y1 = m (x-x1)   ---------------------------(a)

y1=86

x1 = 1

m = (86-84)/(1-2) = -2

now putting the value of y1, x1 and m in eq. (a) we get:

y-86 = -2(x-1)

now since we have to compute for test 4, so x = 4

Therefore, y-86 = -2(4 -1)

=> y-86 = -6

=> y = 80