To find the equation of a line parallel to the given line \( -5x + y = 5 \), we first need to determine the slope of the given line.
- Rewrite the line in slope-intercept form (y = mx + b).
Starting with: \[ -5x + y = 5 \] Add \( 5x \) to both sides: \[ y = 5x + 5 \] The slope \( m \) of the given line is \( 5 \).
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Since parallel lines have the same slope, the slope of the line we want to find will also be \( 5 \).
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Now, we can use the point-slope form of the line equation, which is: \[ y - y_1 = m(x - x_1) \] where \( (x_1, y_1) \) is the point the line passes through, and \( m \) is the slope.
Using the point \( (8, 6) \) and slope \( 5 \): \[ y - 6 = 5(x - 8) \]
- Now, simplify the equation: \[ y - 6 = 5x - 40 \] Add \( 6 \) to both sides: \[ y = 5x - 34 \]
So, the equation of the line parallel to \( -5x + y = 5 \) that passes through the point \( (8, 6) \) is: \[ \boxed{y = 5x - 34} \]
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