Slope and perpendicular lines {ACT}

Which of the following is the equation of a straight line that has y-intercept 3 and is perpendicular to the line 4x - 2y = 6.
A.)  2y + 3x = - 3
B.)  y + 3x = -2
C.)  2y - x = 6
D.)  y - 2x = 4
E.)  2y + x = 6

To find the y-intercept, get each possible answer in slope-intercept form
y = mx + b
m is the slope
b is the y-intercept

Also, perpendicular lines have slopes which are negative reciprocals.  For example 3/2 and -2/3 are negative reciprocals.  Once, the possible answers are in slope-intercept form, you can look at the slope and y-intercept, to decide which one is being asked for.

The given equation in the problem:
4x - 2y = 6
-2y = -4x + 6 {subtracted 4x from both sides}
y = 2x - 3 {divided both sides by -2}
slope = 2 and y-intercept = -3
a perpendicular line to this would have a slope of -1/2

So, out of the possible answers, you are looking for a slope of -1/2 and a y-intercept of 3

A.)  2y + 3x = - 3
2y = -3x - 3 {subtracted 3x from both sides}
y = (-3/2)x - 3/2 {divided both sides by 2}
slope = -3/2 and y-intercept = -3/2

B.)  y + 3x = -2
y = -3x - 2 {subtracted 3x from both sides}
slope = -3 and y-intercept = -2

C.)  2y - x = 6
2y = x + 6 {added x to both sides}
y = (1/2)x + 3 {divided both sides by 2}
slope = 1/2 and y-intercept = 3

D.)  y - 2x = 4y = 2x + 4 {added 2x to both sides}
slope = 2 and y-intercept = 4

E.)  2y + x = 6
2y = -x + 6 {subtracted x from both sides}
y = (-1/2)x + 3 {divided both sides by 2}
slope = -1/2 and y-intercept = 3

The line with a slope of 3 and perpendicular to 4x - 2y = 6 is 
E.)  2y + x = 6

- Algebra House