Question

How do you determine whether each equation is a linear equation: $y=2-3x$?

Answer 1

Hint: A linear equation is an equation in which the highest power of variables present in that equation is equal to 1. Constant may present in a linear equation. But height power can not exceed 1 in any linear equation.

Complete step by step answer:
The given equation is $y=2-3x$
We can see there are 2 variables present in the equation; x and y.
The power of x is 1 and the power of y is also 1, so the highest power in the equation is equal to 1 so the equation is a linear equation.
$\Rightarrow$ Let’s take another example $y=2-3{{x}^{2}}$
We can see that the highest power in the above equation is equal to 2, so it is not a linear equation.
$\Rightarrow$ So the conclusion is if the highest power of a variable in an equation is equal to 1 it is a linear equation.

Note:
The equation given in the question is a linear equation in 2 variables, there may be a linear equation in more than 2 variables. If a system has n variables then we need minimum n equations to evaluate the value of all unknown variables. If less than n equations are there then the total number of solutions may tend to infinity. We can see that in equation $y=2-3x$, 2 variables are there but one equation is present, so we can find an infinite number of pairs (x ,y) that will satisfy $y=2-3x$.