Final answer:
The equation in point-slope form for the line parallel to y=5x-4 that contains the point P(-6,1) is y - 1 = 5(x + 6).
Step-by-step explanation:
The equation of a line that is parallel to another can be found by identifying the slope of the given line and using it in a point-slope form equation incorporating a point that the new line must pass through. In this case, the original line is given by y=5x-4, which means the slope (m) is 5. For a line to be parallel to another, it must have the same slope.
Considering the point P(-6,1) that the new line must pass through, we use the point-slope form, which is (y - y1) = m(x - x1), where (x1, y1) is the point on the line. Plugging in the given point and the identified slope, the equation in point-slope form for the line parallel to y=5x-4 is:
y - 1 = 5(x + 6)
This equation shows the relationship between x and y for any point on the line parallel to the given line and passing through point P(-6,1).