Question

What is the equation of a line perpendicular to 2y = x - 4 and passing through the point (2,1)?

Answer 1

Answer :

y + 2x - 3 = 0

Solution :

Here ,

The given equation of line is 2y = x - 4 which can be rewritten as y = ½•x - 2 .

Clearly ,

y = ½•x - 2 is in of slope y-intercept form y = mx + c , where slope m = ½ .

Now ,

Let the slope of the required perpendicular on the given line be m' .

Since the product of the slopes of perpendicular lines is -1 .

Thus ,

=> m•m' = -1

=> ½•m' = -1

=> m' = -2

Also ,

We know that , the point slope of a straight line passing through (x1 , y1) is given as (y - y1) = Slope•(x - x1)

Thus ,

The equation of the required line passing through point (2 , 1) and have the slope m' = -2 will be given as ;

=> y - y1 = m'(x - x1)

=> y - 1 = -2(x - 2)

=> y - 1 = -2x + 4

=> y - 1 + 2x - 4 = 0

=> y + 2x - 3 = 0

Hence ,

Required line is y + 2x - 3 = 0 .