Cant understand questions below.

Question

Find the equation of a line

A) parallel to the x-axis, passing through (3, -6)

B) perpendicular to y = -2/5x+4 , passing through the origin

C)perpendicular to x= -2, passing through the point (1, -3)

D) perpendicular to y = 4x - 3, passing through the point (-2,7)

Answer 1

a) y=-6 IF it's parallel to the x axis, it has slope = 0

general linear equation is y=mx + b, where m= slope = 0. b= y intercept or the y coordinate of the (0,-6)

y= (0)x -6

y = 0-6

y = -6

b) -2/5 has a negative inverse: 5/2 through the origin means y intercept = 0

y = (5/2)x + 0

y - 5x/2 is the equation of the line perpendicular to y=-2x/5 + 4, through the origin (0,0)

perpendicular to x=-2, through (1,-3)

the equation is y =-3

perpendicular means negative inverse slope: x=-2 has infinite slope, y=-3 has zero slope

y=4x -3 through (-2,7)

a perpendicular line has negative inverse slope: change the sign of 4 and flip it upside down to get -1/4

y=-x/4 +b solve for b by plugging in the point with x=-2 and y=7

7= 1/2 +b

b = 13/2

y =-x/4 + 13/2 is the perpendicular line through the given point

or

x +4y = 26 if you want to remove fractions