Question

What equation represents the line that is perpendicular to y=1/2x - 3 and passes through the point (4,-6)?

Answer 1

The equation of line perpendicular to given line and passing through point (4 , - 6) is y = - 2 x - 2

Explanation:

Given as :

The equation of line is

y =
`(1)/(2)`x - 3

Now, standard equation of line is

y = m x + c

where m is the slope of line and c is the y-intercept

So, comparing with standard line equation with given line equation

∴ slope of given line = m =
`(1)/(2)`

Again

other line is perpendicular to given line and passes through point (4 , - 6)

Let The slope of other line = M

∵ Two lines are perpendicular

∴ From perpendicular lines property , the product of lines = - 1

i.e m × M = -1

Or,
`(1)/(2)` × M = -1

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

∴ M = - 2

So, The slope of other line = M = - 2

Now, equation of line with slope - 2 and points (4 , - 6) in slope-point form

y -
`y_1` = M (x -
`x_1`)

Or, y - ( - 6) = ( -2) × (x - 4)

Or, y + 6 = - 2 x + 4

Or, y = - 2 x + 4 - 6

∴ y = - 2 x - 2

So, The equation of other line is y = - 2 x - 2

Hence, The equation of line perpendicular to given line and passing through point (4 , - 6) is y = - 2 x - 2 Answer