To convert the equation from point-slope form to standard form, we'll start with the point-slope form you provided:
\[ y - 1 = \frac{1}{4}(x - 12) \]
First, let's simplify this equation.
- Distribute the \(\frac{1}{4}\):
\[ y - 1 = \frac{1}{4}x - 3 \]
- Add 1 to both sides to isolate \(y\):
\[ y = \frac{1}{4}x - 2 \]
Now, the equation is in slope-intercept form \(y = mx + b\). To convert it into standard form \(Ax + By = C\), we want the \(x\) and \(y\) terms on one side of the equation and the constant on the other side.
- Multiply every term by 4 to eliminate the fraction:
\[ 4y = x - 8 \]
- Rearranging gives:
\[ x - 4y = 8 \]
Now, we can see that the equation is in standard form. Thus, the standard form of the equation for the line that passes through the points (–4, –3) and (12, 1) is:
\[ \boxed{x - 4y = 8} \]
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