Sure, let's convert the given equation into standard form. The standard form of a linear equation is [tex]\(Ax + By = C\)[/tex].
Given the equation:
[tex]\[ y = 16x + 12 \][/tex]
1. Move the terms involving [tex]\(x\)[/tex] and [tex]\(y\)[/tex] to one side of the equation:
Since we want to get both [tex]\(x\)[/tex] and [tex]\(y\)[/tex] on one side and a constant on the other side, we subtract [tex]\(16x\)[/tex] from both sides:
[tex]\[ y - 16x = 12 \][/tex]
2. Rewrite the equation to match the standard form [tex]\(Ax + By = C\)[/tex]:
Rearrange the equation so that it follows the standard form [tex]\(Ax + By = C\)[/tex]:
[tex]\[ -16x + y = 12 \][/tex]
3. Ensure the coefficient [tex]\(A\)[/tex] is positive:
By convention, the coefficient [tex]\(A\)[/tex] should be positive. If it's not, multiply the entire equation by [tex]\(-1\)[/tex]:
[tex]\[ 16x - y = -12 \][/tex]
Now we have the equation in standard form:
[tex]\[ 16x - y = -12 \][/tex]
Thus, the values for [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] are:
[tex]\[
A = 16, \quad B = -1, \quad C = -12
\][/tex]
