Question

Use the given conditions to write an equation for the line in standard form. 

Passing through (5,-9) and perpendicular to the line whose equation is 2x - 3y = 7

 Write an equation for the line in standard form.

Answer 1

Answer 2

SOLUTION :

Line  to which the required line is perpendicular is given as : 2x - 3y = 7

=> y = 2/3 x - 7/3 

Its slope = 2/3 

Slope of required line perpendicular to it = -1 / (2/3) = - 3/2 .

So, equation of the required line is :

y = - 3/2 x + c 

Since point (5, - 9) is on this line,

- 9 = - 3/2 (5) + c 

=> c = - 9 + 15/2 

=> c = - 3/2

So, equation of the required line is :

y = - 3/2 x - 3/2  

In standard form equation is :

3/2 x + y = - 3/2 

Multiply by 2 .

We get equation in standard form with integers only :

=> 3x + 2y = - 3  (ANSWER).