Certainly! To write the given linear equation in standard form, let's follow these steps:
1. Given Equation:
[tex]\[ 9y = 7x - 8 \][/tex]
2. Rearrange the Equation:
Standard form of a linear equation is given by:
[tex]\[ Ax + By = C \][/tex]
where [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] are integers.
3. Isolate Constants and Variables Appropriately:
To express the equation in the form [tex]\( Ax + By = C \)[/tex], we need to bring all terms to one side of the equation:
[tex]\[ 9y = 7x - 8 \][/tex]
Subtract [tex]\(7x\)[/tex] from both sides to move the [tex]\(x\)[/tex] term to the left side:
[tex]\[ -7x + 9y = -8 \][/tex]
4. Standard Form:
Generally, the coefficient of [tex]\( x \)[/tex] (i.e., [tex]\( A \)[/tex]) in the standard form is positive. We can multiply the entire equation by [tex]\(-1\)[/tex] to achieve this, but it is conventional to keep all coefficients as is if they meet the requirement that [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] are integers.
So:
[tex]\[ 7x - 9y = 8 \][/tex]
Therefore, the constants are:
[tex]\[ A = 7 \][/tex]
[tex]\[ B = -9 \][/tex]
[tex]\[ C = 8 \][/tex]
The standard form of the given equation [tex]\( 9y = 7x - 8 \)[/tex] is:
[tex]\[ 7x - 9y = 8 \][/tex]
