Question

Give the equation of the line that is perpendicular to y= (1/2)x -1 and passes through the point (3,4)

Answer 1

Answer: y = -2x + 10

Explanation:

Two lines are said to be perpendicular if the product of their slope = -1, that is , if
`m_(1)` is the slope of the first line and
`m_(2)` is the slope of the second line , if the two lines are perpendicular , then
`m_(1)`
`m_(2)` = -1

The equation of the line given :

y = 1/2x - 1

comparing with the equation of line in slope intercept form

y = mx + c , where m is the slope and c is the y - intercept , it implies that

`m_(1)` = 1/2

Therefore :

`m_(2)` = -2

To find the equation of the line with slope -2 and passes through the point ( 3 , 4 ) we will use the formula

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

y - 4 = -2 ( x - 3 )

y - 4 = -2x + 6

y = -2x + 6 + 4

y = -2x + 10