To express the equation [tex]\( \frac{x}{4} - 3y = -7 \)[/tex] in the form [tex]\( ax + by + c = 0 \)[/tex], we need to perform a few algebraic steps.
### Step-by-Step Solution:
1. Eliminate the Fraction:
First, let's eliminate the fraction by multiplying each term of the equation by 4:
[tex]\[
4 \left(\frac{x}{4}\right) - 4 \cdot 3y = 4 \cdot (-7)
\][/tex]
2. Simplify:
This simplifies to:
[tex]\[
x - 12y = -28
\][/tex]
3. Rearrange into the Standard Form [tex]\(ax + by + c = 0\)[/tex]:
To rearrange it into the required form [tex]\( ax + by + c = 0 \)[/tex], we need to move the constant term to the left-hand side of the equation:
[tex]\[
x - 12y + 28 = 0
\][/tex]
### Conclusion:
The equation [tex]\( \frac{x}{4} - 3y = -7 \)[/tex] expressed in the form [tex]\( ax + by + c = 0 \)[/tex] is:
[tex]\[
x - 12y + 28 = 0
\][/tex]
Here, the coefficients are:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = -12 \)[/tex]
- [tex]\( c = 28 \)[/tex]
Thus, the standard form of the given equation is [tex]\( x - 12y + 28 = 0 \)[/tex].
