To find the equation of a line in standard form \(Ax + By = C\), we can start with the point-slope form of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
where \(m\) is the slope, and \((x_1, y_1)\) is a point on the line. Here, the slope \(m = -12\) and the point given is \((4, 6)\).
Substituting the values into the point-slope form:
\[ y - 6 = -12(x - 4) \]
Now, simplify and rearrange to get the equation in standard form.
- Distributing \(-12\):
\[ y - 6 = -12x + 48 \]
- Adding 6 to both sides:
\[ y = -12x + 54 \]
- Rearranging to get standard form by moving all terms to one side:
\[ 12x + y = 54 \]
Thus, the equation in standard form is:
\[ 12x + y = 54 \]
So, the answer is:
\[ A = 12, \quad B = 1, \quad C = 54 \]
In the form \(x + y = C\), we have to rearrange it:
Divide the entire equation \(12x + y = 54\) by \(12\) if needed, to put it in \(x + y = C\):
\[ x + \frac{y}{12} = \frac{54}{12} \]
However, if you want to keep it in the standard form:
\[ 12x + y = 54 \]
That's the standard form solution you need!