Question

A

What is the slope of a line perpendicular to
x + 2y = 4? [2 marks] - Show ALL work
A 2
B 1/2
C -2
D-1/2

Answer 1

A

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

x + 2y = 4 ( subtract x from both sides )

2y = - x + 4 ( divide terms by 2 )

y = -
`(1)/(2)` x + 2 ← in slope- intercept form

with slope m = -
`(1)/(2)`

Given a line with slope m then the slope of a line perpendicular to it is

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

Answer 2

To start, the equation has to be converted to slope-intercept form, or
`y=mx+b`. Start by subtracting x from both sides;
`x-x+2y=4`,
`2y=4-x`. Switch 4 and -x around to conform to the formula;
`2y=-x+4`. Then divide by 2 to isolate y;
`y=-(1)/(2)x+2`. This is the final equation. Because the slope of a line perpendicular is always the opposite reciprocal (i.e. The opposite reciprocal of 4 is
`-(1)/(4)`, the opposite reciprocal of
`-(1)/(5)` is 5) the opposite reciprocal of
`-(1)/(2)` is 2. So the equation of the line is
`y=2x`, and the answer is A.