To find the equation of a line that is parallel to the line \( y = 25x + 1 \), we first note that parallel lines have the same slope. The slope of the given line is 25.
Now, we use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope, and \( (x_1, y_1) \) is the point through which the line passes. In this case, \( m = 25 \) and \( (x_1, y_1) = (5, 5) \).
Plugging these values into the point-slope equation:
\[ y - 5 = 25(x - 5) \]
Now, simplify this equation:
\[ y - 5 = 25x - 125 \]
Adding 5 to both sides gives:
\[ y = 25x - 120 \]
Thus, the equation of the line that is parallel to \( y = 25x + 1 \) and passes through the point \( (5, 5) \) is:
\[ y = 25x - 120 \]
So in the format requested:
The line that is parallel to \( y = 25x + 1 \) and passes through the point \( (5,5) \) is \( y = 25x - 120 \).
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