Question

How do you write $y = 3x + 8$ in standard form?

Answer 1

Hint: In this question, we want to write the given expression in standard form. The standard form of the linear equation of two variables is $ax + by = c$. Where ‘a’ is the coefficient of x, ‘b’ is the coefficient of y, and ‘c’ is the constant term. Here, a, b, and c are integers, and ‘a’ is non-negative. And x and y are variables. The linear equation has only the first power.

Complete step-by-step answer:
In this question, we want to write the given expression in standard form, and the given expression is:
$ \Rightarrow y = 3x + 8$
Let us subtract 3x on both sides.
$ \Rightarrow - 3x + y = 3x + 8 - 3x$
The subtraction of 3x and 3x is 0 on the right-hand side.
That is equal to,
$ \Rightarrow - 3x + y = 8$
Now, multiply both sides by -1 to convert the equation in the standard form.
$ \Rightarrow \left( { - 1} \right)\left( { - 3x + y} \right) = 8\left( { - 1} \right)$
Now, remove the bracket on the left-hand side and multiply the bracket with -1.
$ \Rightarrow \left( { - 1} \right)\left( { - 3x} \right) + \left( { - 1} \right)\left( y \right) = 8\left( { - 1} \right)$
That is equal to,
$ \Rightarrow 3x - y = - 8$
As we know the standard form of the linear equation is $ax + by = c$.
In this linear equation, the value of ‘a’ is 3, the value of ‘b’ is -1 and the value of ‘c’ is -8.
Hence, the standard form of the given equation is $3x - y = - 8$ .

Note:
In the linear equation a, b, and c have no common factors other than 1. The standard form of an equation is useful for finding the x and y-intercepts of a graph. That is the point where the graph crosses the x-axis and the point where it crosses the y-axis. The standard form of an equation is useful for finding the points where two or more functions intersect.