Question

Give the equation of the line, perpendicular to the line with equation y=2x+1, that passes

through the point (8,-2).

Answer 1

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

Explanation:

The equation of a line in slope- intercept form is

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

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

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

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

y = -
`(1)/(2)` x + c ← is the partial equation

To find c substitute (8, - 2) into the partial equation

- 2 = - 4 + c ⇒ c = - 2 + 4 = 2

y = -
`(1)/(2)` x + 2 ← equation of perpendicular line

Answer 2

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

Explanation:

When two lines are perpendicular their slopes are negative reciprocals. So, if the slope of the first line is 2, then the slope of the line perpendicular to it is
`-(1)/(2)`.

To find the y-intercept, input the slope and the given point (8, -2) into the equation y = mx + b and solve for b:

`-2 = -(1)/(2)(8)+b`

-2 = -4 + b

2 = b

The y-intercept is 2.

Now that we know the slope and the y-intercept, we can write the equation:

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

Hope this helps :)