Question

6. f(x) is a linear function with a slope of 1/2. f(4) = 3. Find f(x) in standard form.

Answer 1

ANSWER

$\frac{1}{2}x\text{ - f(x) = -1}$

EXPLANATION

We are given that the function has a slope of 1/2.

First, we have to write this equation in slope intercept form.

To do that, use the point-slope method:

f(x) - f(x1) = m(x - x1)

where m = slope

(x1, f(x1)) is a point that satisfies the equation.

From the question:

f(4) = 3

This means that when x = 4, f(x) = 3

Therefore, (x1, y1) = (4, 3)

Therefore:

$\begin{gathered} f\mleft(x\mright)-3\text{ = }\frac{1}{2}(x\text{ - 4)} \\ \text{Simplify:} \\ f(x)\text{ - 3 = }\frac{1}{2}x\text{ - 2} \\ f(x)\text{ = }\frac{1}{2}x\text{ - 2 + 3} \\ f(x)\text{ = }\frac{1}{2}x\text{ + 1} \end{gathered}$

A linear equation written in standard form is written as:

Ax + Bf(x) = C

Let us put this equation in this form:

$\frac{1}{2}x\text{ - f(x) = -1}$

That is the answer.