Consider the line y= 8x-4 .
Find the equation of the line that is parallel to this line and passes through the point (3,-6) .
Find the equation of the line that is perpendicular to this line and passes through the point (3,-6).
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you know that the equation of parallel lines are similar. the only difference is the y-intercept
so the equation of the required parallel line will be y = 8x + c
now as the line passes through (3, -6) it will satisfy the equation
so -6 = 8(3)+c
c = -6-24
so the required equation is y = 8x -30
now for perpendicular lines, the slope of the required line multiplied by the slope of the given line = -1
from here find the slope of the required line
you have slope and one point, so you can find the equation of the line