Question

How do you write \[y = 3x + 1\] in standard form using integers?

Answer 1

Hint: We are given an equation and asked to write its standard form using integers. Observe the equation and identify what type of equation is this and recall the standard form for such type of equation. Then try to transform the given equation into the standard form.

Complete step-by-step answer:
Given the equation \[y = 3x + 1\] .
We are asked to write this equation in standard form using integers.
The given equation is a linear equation of two variables.
The standard form of a linear equation of two variables is,
 \[Ax + By = C\] (i)
where \[A\] , \[B\] and \[C\] are integers such that \[A\] is a positive integer and \[A\] , \[B\] and \[C\] do not have any common factor other than \[1\] .
Now, we will transform the given equation \[y = 3x + 1\] into standard form as in equation (i)
We have,
 \[y = 3x + 1\] (ii)
We subtract \[ - 3x\] from both sides of the above equation so that the variables \[x\] and \[y\] come on the same side. Subtracting \[ - 3x\] from both sides of equation (ii) we get,
 \[ - 3x + y = 3x + 1 - 3x\]
 \[ \Rightarrow - 3x + y = 1\]
Multiplying both sides by \[ - 1\] we get,
 \[\left( { - 1} \right)\left( { - 3x + y} \right) = \left( { - 1} \right)1\]
 \[ \Rightarrow 3x - y = - 1\]
Therefore, the above equation matches with the standard form of linear equation.
Hence, the standard form of \[y = 3x + 1\] is \[3x - y = - 1\]
So, the correct answer is “3x - y = - 1”.

Note: The equation given is a linear equation of two variables. Linear equations can be defined as equations that are of first order or we can say equations in which the highest power of its variables is one. In the given equation power of both the variable \[x\] and \[y\] is one so, it is a linear equation. The equation of a straight line is also a linear equation with two variables.