Question

Write the equation of a line perpendicular to 5x – 4y = - 3 that passes through the point (-5,2).

The equation of the line is y =

Answer 1

Answer: 5y + 4x = - 10

Explanation:

Two lines are said to be perpendicular if the product of their gradients = -1.

If the gradient of the first line is
`m_(1)` and the gradient of the second line is
`m_(2)` , if the lines are perpendicular, them

`m_(1)` x
`m_(2)` = -1 , that is

`m_(1)` =
`(-1)/(m_(2) )`

The equation of the line given is 5x - 4y = -3 , we need to write this equation in slope - intercept form in order to find the slope.

The equation in slope -intercept form is given as :

y =mx + c , where m is the slope and c is the y - intercept.

Writing the equation in this form , we have

5x - 4y = + 3

4y = 5x -+3

y = 5x/4 + 3/4

comparing with the equation y = mx + c , then
`m_(1)` = 5/4

Which means that
`m_(2)` = -4/5 and the line passes through the point ( -5 , 2 ).

Using the equation of line in slope - point form to find the equation of the line;

y -
`y_(1)` = m ( x -
`y_(1)` )

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

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

5y - 10 = -4x - 20

5y + 4x = - 10