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

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*