Given a table that shows values for a linear function, f(x). we are asked to determine the equation of f(x).
Table:
x f(x)
-1 -8
3 -5
7 2
11 1
First, let us consider the lines of the equation as:
f(x) = ax + b
When x = -1 f(x) = -8
f(-1) = a(-1) + b
-8 = -a + b ------------------ eqn I
When x = 3 f(x) = 5
f(3) = a(3) + b
-5 = 3a + b ------------------- eqn II
subtract eqn I from eqn II:
-5 - (-8) = (3a + b) - (-a + b)
-5 + 8 = 3a + b + a - b
3 = 4a (-b and +b cancels out).
divide both sides by 4:
a = 3/4
Let's put the value of a = 3/4 into equation I
-8 = -a + b
-8 = -3/4 + b
make b the subject of formula:
b = -3/4 + 8
b = -32 + 3
4
b = -29/4
Let's now place the values of a an b into the lines equation:
recall the lines equation is :
f(x) = ax + b
f(x) = 3/4 x - 29/4.