Question

How do you determine whether $y = 2x - 1$ is a linear equation. If so, write the equation
in standard form?

Answer 1

As we know that a linear equation is an algebraic equation of the form $y = mx + b$, involving only a constant and a first order (linear) term, where $m$is the slope and $b$is the $y$-intercept. These have the order equal to unity or one. The linear equation in one variable is written in standard form as $ax + b = 0$i.e. only one variable. It is classified into different types based on the number of variables like linear equations in one variable or linear equations in two variables.

Complete step by step solution:
The equation of a straight line can be written in several forms . $y = mx + b$is one of the form of
linear equation. And we have $y = 2x - 1$ is in this form, therefore it is a linear equation.
We know that it has an $x$term, a $y$term and a constant. We will rearrange it to get the standard
form: $2x - y = 1$.

Hence the answer is “yes”, it is a linear equation and the standard form is $2x - y = 1$.

Note: We can also write the equation in some other standard form i.e. $2x - y - 1 = 0$. This is also the correct way to write it as it can be written in many ways. The slope intercept form of the above equation is $y = 2x - 1$. Also if we make the graph of the linear equation it will have a straight line, this will happen when the highest power of $x$is $1$ . There are many ways a linear equation can be written but they usually have like $2$or $c$and must have simple variables like $x$or $y$.