Consider the line $y=6 x-9$
Find the equation of the line that is perpendicular to this line and passes through the point $(8,-4)$. Find the equation of the line that is parallel to this line and passes through the point $(8,-4)$.
Equation of perpendicular line:
Equation of parallel line:

Step 1 ：The slope of the given line is 6. The slope of a line perpendicular to this line would be the negative reciprocal of 6, which is -1/6. The slope of a line parallel to this line would be the same as the slope of the given line, which is 6.

Step 2 ：We can use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Step 3 ：For the perpendicular line, we can substitute m = -1/6 and (x1, y1) = (8, -4) into the point-slope form to get the equation of the line.

Step 4 ：For the parallel line, we can substitute m = 6 and (x1, y1) = (8, -4) into the point-slope form to get the equation of the line.

Step 5 ：Final Answer: The equation of the line that is perpendicular to the line \(y=6 x-9\) and passes through the point \((8,-4)\) is \(y=-\frac{1}{6}x - \frac{8}{3}\).

Step 6 ：The equation of the line that is parallel to the line \(y=6 x-9\) and passes through the point \((8,-4)\) is \(y=6x - 52\).