Question

How do you change $y=7x+10$ into standard form?

Answer 1

Hint: The standard form of the equation is $ax+by=c.$ We rearrange the given equation to convert it into the standard form. The rearrangement is done by transposing the terms accordingly.

Complete step by step solution:
We say an equation is in its standard form if it is in the form $ax+by=c.$
In this equation, $a,b$ and $c$ are any real numbers and $x$ and $y$ are two independent variables.
Consider the given algebraic equation $y=7x+10.$
This is an equation in two variables $x$ and $y.$
To change this equation into its standard form, we need to transpose the term containing from the right-hand side of the equation to the right-hand side of the equation.
The term to be transposed is $7x.$
When we transpose the terms, the sign of the terms to be transposed will get changed. If the term is positive, then it will be changed to negative and if the sign of the terms is negative, then it will get changed to positive.
Since the sign of the term $7x$ is positive, the sign will get changed to negative after it is transposed to the left-hand side. That is, it will become $-7x.$ The signs of the rest of the terms will remain as they are.

Hence the standard form of the given algebraic equation is $y-7x=10.$

Note: We often forget to change the sign of the terms while we transpose them. Like the signs of the terms, the operations used also get changed. Addition will be changed to subtraction and vice versa. Multiplication will be changed to division and vice versa.