If f(x) is a linear function such that f(2) =5 and f(4)=13, then f(x) =

A. f(x) = 3x−4

B. f(x) = 4x−3

C. f(x) = 4x+3

D. f(x) = ¼x + 9/2

E. f(x) = ¼x - 9/2

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Solution
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The solution will be done in the following steps:

*Step 1:* Find the gradient.

*Step 2:* Find the y-intercept.

*Step 3:* Substitute the slope and the y-intercept in the equation for the line and solve

Let's get started....

The statement, "f(2) =5 and f(4)=13"
, means that:
x1 = 2, y1 = 5
x2 = 4, y2 = 13

Gradient = (y2 - y1)/(x2 - x1)
= (13-5)/(4-2)
= 8/2
= 4

Gradient = 4.

Using the general equation of a straight line
f(x) = mx + c

Where m is the gradient and c is the y-intercept.

Putting m = 4 gives

f(x) = 4x + c

....but we are given that f(2) = 5, then it follows that

f(2) =
4×2 + c = 5

8 + c = 5

c = -3

Putting the values of m and c in the general equation of a straight line, f(x) = mx + c gives:

f(x) = 4x - 3

The correct option is B.

Source: http://samimath.com/q-equation-straight-line/

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