Question

Find an equation of the line that passes through the point (4, 2) and is perpendicular to the line 2x + 5y 6 = 0 Need Help? Talk to a Tutor Read It

Answer 1

Given point is (4,2)

Perpendicular line is 2x+5y-6=0

Slope of the line ax+by+c=0 is $-\frac{a}{b}$

Let m₁ be the slope of given line and m₂ be the slope of the required perpendicular line.

So

2 m1 5

For perpendicular lines, Product of the slope=-1

m₁ * m₂ =-1

2 * т2 3 — 1 5

-5 m2-1 * (. 2

m2

So slope of the required line is 5/2 and the point is (4,2)= (x₁ , y₁ )

Now equation of line passing though a point (x₁ , y₁ ) and having slope m is given by

y-y₁ =m(x-x₁)

5 y 2 ( 4) 2

2(y-2) =5(x-4)

2y-4=5x-20

5x-2y-20+4=0

5x-2y-16=0

So 5x-2y-16=0 is the equation of the line passing through (4,2) and perpendicular to 2x+5y-6=0