Question

rewrite the following equation in standard form.
$y = 4x + 8$
hint: the standard form of a linear equation is $ax + by = c$ where a and b are not both zero, and a, b, and c are integers whose gcf is 1.

Explanation:

Step1: Move 4x to the left

To get the equation in standard form \(Ax + By = C\), we subtract \(4x\) from both sides of the equation \(y = 4x + 8\).
\(y - 4x = 4x + 8 - 4x\)

Step2: Simplify the equation

Simplifying the right side, we get \(y - 4x = 8\). We can also write it as \(-4x + y = 8\). To make \(A\) positive (though not strictly necessary, but following the common convention), we can multiply both sides by -1, but in this case, the GCF of -4, 1, and 8 is 1, and we can also leave it as \(-4x + y = 8\) or rearrange to \(4x - y = -8\) (multiplying both sides by -1: \((-1)(-4x + y)=(-1)(8)\) gives \(4x - y = -8\)). However, starting from the first step of moving \(4x\) to the left, we have:
From \(y = 4x + 8\), subtract \(4x\) from both sides:
\(-4x + y = 8\) (or \(4x - y = -8\), both are in standard form. Let's check the GCF: for \(-4x + y = 8\), GCF of -4, 1, 8 is 1; for \(4x - y = -8\), GCF of 4, -1, -8 is 1 as well. But let's follow the steps as per the hint. The standard form is \(Ax + By = C\), so let's rearrange \(y = 4x + 8\) to \(Ax + By = C\) by moving \(4x\) to the left:
\(-4x + y = 8\) (or \(4x - y = -8\)). Let's verify:
For \(-4x + y = 8\), \(A=-4\), \(B = 1\), \(C = 8\). GCF of -4, 1, 8 is 1. For \(4x - y = -8\), \(A = 4\), \(B=-1\), \(C=-8\), GCF of 4, -1, -8 is 1. Either is correct, but let's do the step - by - step as:

Starting with \(y = 4x + 8\)

Subtract \(4x\) from both sides:

\(y-4x=4x + 8-4x\)

Simplify right side: \(y - 4x=8\)

Which can be written as \(-4x + y = 8\) (or \(4x - y=-8\))

Answer:

\(-4x + y = 8\) (or \(4x - y=-8\)) (both are correct, but a more common form with positive \(A\) is \(4x - y=-8\) or keeping \(A\) as - 4: \(-4x + y = 8\))