Question

Which equations represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5,-4)? Select

three options.

Answer 1

WRONG!

y = –Two-fifthsx – 2 * correct

2x + 5y = −10 * Correct

2x − 5y = −10

y + 4 = –Two-fifths(x – 5) * Correct

y – 4 = Five-halves(x + 5)

Explanation:

Answer 2

The equation of line passing through points (5 , - 4) is 2 x + 5 y + 10 = 0

Explanation:

Given equation of line as

5 x - 2 y = - 6

Now, equation of line in standard form is y = m x + c

where m is the slope

So, 5 x - 2 y = - 6

Or, 2 y = 5 x + 6

Or, y =
`(5)/(2)` x + 3

So, Slope of this line m =
`(5)/(2)`

Again , let the slope of other line passing through point (5 , - 4) is M

And Both lines are perpendicular , So , products of line = - 1

i.e m × M = - 1

Or, M = -
`(1)/(m)`

Or, M = -
`(1)/((5)/(2))` = -
`(2)/(5)`

So, equation of line with slope M and points (5, - 4) is

y -
`y_1` = M × (x -
`x_1`)

Or, y - ( - 4 ) = -
`(2)/(5)` × ( x - 5 )

Or, y + 4 = -
`(2)/(5)` x +
`(2)/(5)` × 5

Or, y + 4 = -
`(2)/(5)` x + 2

or, y + 4 - 2 = -
`(2)/(5)` x

or, y + 2 = -
`(2)/(5)` x

Or, 5×(y + 2) = - 2 x

∴ 5 y + 10 = - 2 x

I.e 2 x + 5 y + 10 = 0

Hence The equation of line passing through points (5 , - 4) is 2 x + 5 y + 10 = 0 Answer