Find the equation of a line that goes through the point ( 1, - 1 ) and is parallel to the line y = - 6x + 1

Step 1: Identify the slope of the given line The equation of the given line is in the form y = mx + b, where m is the slope. Here, m = -6.

Step 2: Use the slope of the parallel line Parallel lines have the same slope. So, the slope of the line we want to find is also -6.

Step 3: Use the point-slope form of a line The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We know that our line passes through the point (1, -1) and has a slope of -6. So, we can substitute these values into the point-slope form:

y - (-1) = -6(x - 1)

Step 4: Simplify the equation Simplify the equation to put it in the slope-intercept form (y = mx + b):

y + 1 = -6x + 6 y = -6x + 6 - 1 y = -6x + 5

So, the equation of the line that goes through the point (1, -1) and is parallel to the line y = -6x + 1 is y = -6x + 5.