Courses
Courses for Kids
Free study material
Offline Centres
More
Store

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

Last updated date: 13th Jun 2024
Total views: 372.3k
Views today: 8.72k
Verified
372.3k+ views
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.