Question

How do you write\[\;y = 4x - 11\] in standard form?

Answer 1

Hint: Here in this given equation is a linear equation. we have to write the given equation in the standard form of a linear equation\[Ax + By = C\]. By simplifying the basic arithmetic operation i.e., addition, subtraction and multiplication we get the required solution for the above equation.

Complete step-by-step solution:
The given equation is a linear equation. These equations are defined for lines in the coordinate system. An equation for a straight line is called a linear equation i.e., \[y = mx + b\], where m is the slope and b is the y-intercept. Occasionally, this equation is called a "linear equation of two variables," where y and x are the variables. The general or standard representation of the straight-line equation is \[Ax + By = C\], it involves only a constant term and a first-order (linear) term.

Consider the given equation
\[ \Rightarrow \,\,\,\,\;y = 4x - 11\]
Move all terms containing variables to the left side of the equation. i.e., we have to shift the variable x and its coefficient to the LHS, by subtract -4x on both sides, then
\[ \Rightarrow \,\,\,\,\;y - 4x = 4x - 11 - 4x\]
On simplification we get
\[ \Rightarrow \,\,\,\,\;y - 4x = - 11\]
Multiply both sides by -1.
\[ \Rightarrow \,\,\,\,\; - 1\left( {y - 4x} \right) = - 1\left( { - 11} \right)\]
\[ \Rightarrow \,\,\,\,\; - y + 4x = 11\]
Rewrite the equation with the variables x and y flipped.
\[ \Rightarrow \,\,\,\,\;4x - y = 11\]
Hence, the standard form of the given linear equation \[\;y = 4x - 11\] is \[4x - y = 11\].

Note: The general or standard representation of the straight-line equation is \[Ax + By = C\], it involves only a constant term and a first-order (linear) term. While shifting or transforming the term in the equation we should take care of the sign. Here sign conventions are used in this problem.