Find the perpendicular line equation?

Question

Write an equation of a line through (4, 5) that is perpendicular to y = 1/2x + 3

Answer 1

Given that equation of line is passing through (4 , 5)

And also given that line is perpendicular to y = (1/2)x + 3

Slope of the given line is (m1) = 1/2

Slope of the required line is m1 * m2 = -1

1/2 * m2 = -1

m2 = -2

Equation of the line pasing through two points is y = mx + c

(x , y) = (4 , 5) and m = -2

5 = (-2)(4) + c

5 = -8 + c

5 + 8 = c

c = 13

Therefore the required line equation is y = -2x + 13
 

Answer 2

The line of the equation : y =(1/2)x+3

The slope the line say m1 = 1/2

Equation to a line through the point (x1,y1) is y-y1 = m (x-x1)

The given point (x1,y1) = (4,5)

Substitute the point

y-5 = m2 (x-4)

To find m2

Perpendicular lines must obey the rule,product of two lines slope is equal to -1

m1m2 = -1

1/2(m2) = -1

m2 = -1(2)

m2 = -2

So the perpendicular line equation is y-5 = -2(x-4)

y-5 = -2x+8

y = -2x+8+5

y = -2x+13