Writing equations of lines parallel and perpendicular to a given line through a point

Question

Consider the line x - 4y = -6

Find the equation of the line that is perpendicular to this line and passes through the point (−1,  1)

Find the equation of the line that is parallel to this line and passes through the point (−1,  1)

Answer 1

x-4y = -6

-4y = -x -6

4y = x +6

y = (1/4)x + 3/2

any parallel line has the same slope = the coefficient of the x term when the linear euation is solved for y. slope = 1/4

any perpendicular line has slope = the negative inverse = -4

a perpendicular line through (-1,1) would be

y-1 = -4(x+1)

or

y = -4x -3 in slope intercept form

or

4x +y + 3 = 0 in general form

or

4x +y =-3 in standard form

a parallel line through (-1,1) would be

y-1 = (1/4)(x+1)

or

y = x/4 +5/4 in slope intercept form

or

x +4y +5 = 0 in general form

or

x-4y =-5 in standard form