91Ó°ÊÓ

Alinear equationis anyequationthat can be written in the form$ax+by=0$, where a and b are real numbers and x is a variable. This form is sometimes called the standard form of a linear equation.

No variable in alinear equationis raised to a power greater than 1. Linear equationsare those equations that are of the first order.

Standard form of Linear Equation is$Ax+By+C\text{ â¶Ä‰}=\text{ â¶Ä‰}0$, where A, B and C are any integer.

In order to rewrite the equation $\frac{1}{4}x−\frac{3}{4}y=−1$ in standard form multiply each term of the equation by 4.

$$\begin{gathered} \frac{1}{4}x−\frac{3}{4}y=−1 \\ 4â‹\dots \frac{1}{4}x−4â‹\dots \frac{3}{4}y=−1â‹\dots 4 \\ 4x−12y=−4 \\ 4x−12y+4=−4+4\text{ [ Add 4 â¶Ä‰to â¶Ä‰both â¶Ä‰sides ]} \\ 4x−12y+4=0 \end{gathered}$$

The equation is now in standard form where$A=4,B=−12\text{and}C=4$. Since the variables in the equation has the highest exponent as 1, so the equation is linear.

Yes, this is a linear equation and the standard form is:$4x−12y+4=0$.