Question

convert $y = 4x - 7$ into standard form.
a. $4x - y = -7$
b. $4x - y = 7$
c. $-4x + y = -7$
d. $-4x + y = 7$

Explanation:

Step1: Recall standard form

The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\geq0\).

Step2: Start with given equation

We have the equation \(y = 4x - 7\). To convert it to standard form, we need to get the \(x\) and \(y\) terms on the left side and the constant on the right side. Subtract \(4x\) from both sides:
\(y - 4x = 4x - 7 - 4x\)
Simplifying the right side gives \(y - 4x = -7\).

Step3: Rearrange terms

We can rewrite \(y - 4x = -7\) as \(-4x + y = -7\), but we usually want \(A\) (the coefficient of \(x\)) to be positive. Multiply both sides of \(-4x + y = -7\) by \(-1\):
\((-1)(-4x + y) = (-1)(-7)\)
Which simplifies to \(4x - y = 7\).

Answer:

b. \(4x - y = 7\)