Question

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).

Answer 1

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
c= -30

so the required equation is y = 8x -30

Answer 2

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