Question

An equation that defines $y$ as a function of $x$ is given. Solve for $y$ in terms of $x$, and replace $y$ with the function notation $f(x)$ .
$x - 2y = 18$
A. $f(x) = \dfrac{1}{2}x - 18$
B. $f(x) = \dfrac{1}{2}x - 9$
C. $f(x) = - x + 9$
D. $f(x) = - \dfrac{1}{2}x + 9$

Answer 1

Hint: When we solve the linear equation in two variables and for $y$ in terms of $x$ , then we can write $y$ as $f(x)$ i.e., the function of $x$. Here we just need to keep x on one side and y on the other side. From this we will get y in the form of x which is our required answer. These types of questions are real-time examples of linear equations in two variables. For linear equations in two variables, there are infinitely many solutions.

Complete step-by-step answer:
We have the equation in two variables as $x - 2y = 18$.
First, we will take $y$ on one side and other variables on the other sides, and find the value of $y$.
$x - 2y = 18$
$x - 18 = 2y$
Rearranging the terms,
$2y = x - 18$
Taking the $2$ to the denominator on right hand side,
$y = \dfrac{{x - 18}}{2}$
Splitting the denominator,
$y = \dfrac{x}{2} - \dfrac{{18}}{2}$
$y = \dfrac{1}{2}x - 9$
We have got the value of $y$ in terms of $x$.
Now we will replace $y$ as a function of $x$, i.e., $f(x)$
$f(x) = \dfrac{1}{2}x - 9$
Therefore, the correct option is option B. $f(x) = \dfrac{1}{2}x - 9$

So, the correct answer is “Option B”.

Note: An equation is said to be a linear equation in variables if it's far written within the form of $ax + by + c = 0$ , in which $a,b,c$ are real numbers and the coefficients of $x$ and $y$, i.e., $a$ and $b$ respectively, are not identical to $0$. For the given linear equations in two variables, the solution could be precise for both the equations, if and best if they intersect at a single factor. The condition to get the particular solution for the given linear equations is, the slope of the line fashioned by the $2$ equations, respectively, should no longer be identical.