Write an **equation of the line ** perpendicular to the line of x – 2y – 6=0 and passing through A(-3,2). How to verify my answer.

1 Answers

First, convert given

2y = x – 6

y = (1/2)x – 3

**equation of a line**x – 2y – 6 = 0 into**slope intercept form**y = mx + c, where m is the slope of a line.2y = x – 6

y = (1/2)x – 3

After comparing both equations, we get the slope m_{1} = 1/2

Now, if m_{2} is the slope of perpendicular line then condition ** two lines are perpendicular** is m

_{1}m

_{2}= -1 or m

_{2}= -1/m

_{1}.

Since,

m

_{1}= 1/2

m

_{2}= -2

Now, we find the equation of a line which is passing through the point (a, b) and slope is m is y – b = m(x – a)

Here,

Point is (-3,2) and slope is m = -2, Therefore,

y – 2 = -2[x – (-3)]

y – 2 = -2[x + 3]

y – 2 = -2x – 6

y + 2x = -6 + 2

y + 2x = -4

2x + y = -4

Hence, the **equation of a perpendicular line **is 2x + y = -4.

Please login or Register to submit your answer