Question

How do you write \[y + 1 = x + 2\] in standard form?

Answer 1

Hint: The standard form of a linear equation in two variables is \[ax + by + c = 0\], where \[a\], \[b\] and \[c\] are constants or integers. Here, \[a\] is the coefficient of \[x\], \[b\] is the coefficient of \[y\] and \[c\] is the constant independent term.

Complete step by step solution:
The given equation is \[y + 1 = x + 2\].

From the given equation it is observed that the equation has two variables \[x\] and \[y\].

Also it is observed that the highest power of any variable either variable \[x\] or variable \[y\] in the equation is one.

We know that if the highest power of variables is one in the equation, then these equations are called linear variable equations.

So, the given equation has two variables with the highest power of variables is 1. Therefore, the given equation is a linear equation in two variables.

The standard form for the linear equation in two variables is written as \[ax + by + c = 0\] where \[a\], \[b\] and \[c\] are constants or integers.

In the question, our objective is to write the given equation \[y + 1 = x + 2\] in standard form which is \[ax + by + c = 0\] in linear equations in two variables equation cases.

Let’s convert the given equation in standard form as shown below.

Subtract the number \[2\] from both sides of the equation as follows:
\[y + 1 - 2 = x + 2 - 2\]
\[ \Rightarrow y - 1 = x\]

Now, subtract the variable \[x\] from both sides of the equation as follow:
\[y - 1 - x = x - x\]
\[ \Rightarrow y - 1 - x = 0\]

Now, rearrange the equation as shown below.
\[ - x + y - 1 = 0\]

We can write the given equation as \[\left( { - 1} \right)x + \left( 1 \right)y + \left( { - 1} \right) = 0\] where \[a = - 1\], \[b = 1\] and \[c = - 1\].

Thus, the standard form of the given equation can be written as \[ - x + y - 1 = 0\].

Note: The standard form of the linear equation in two variables \[ax + by + c = 0\], where \[a\], \[b\] and \[c\] are constants or integers is not unique. It depends on the representation of the equation chosen by a student.