Question

find an equation for the line that passes through the point (7,1) and is perpendicular to the line x-3y+25=0​

Answer 1

y + 3x = - 20

Explanation:

x - 3y + 25 = 0

- 3y = - 25 - x

3y = 25 + x

y = ( 25 + x )/3

y = ( 1/3 )x + 25/3

Y= mX+ c

m= gradient= 1/3

The perpendicular gradient should be the negative reciprocal of the gradient we have now.

which is : -1÷(1/3) = -3

Now for the perpendicular line equation, we have:

y = 1

x= 7

m= -3

y - y1 = m ( x - x1 )

y - 1 = -3 ( x + 7 )

y-1 = -3x -21

y + 3x = -20