Question

1. Another line k is perpendicular to line j and passes through

The equation for line j can be written as y =1/2x-1
the point (6, -6). Choose the equation for line k.

Answer 1

The equation for line k is
`y = -2x + 6`

Explanation:

The equation of a line has the following format:

`y = mx + b`

In which m is the slope.

When two lines are perpendicular, the multiplication of their slopes is -1.

The equation for line j can be written as y =1/2x-1

Since k is perpendicular to j, and the slope of j is 1/2, the slope of k is:

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

`m = -2`

So

`y = -2x + b`

It passes through the point (6,-6).

This means that when
`x = 6, y = -6`. So

`y = -2x + b`

`-6 = -2(6) + b`

`b = 6`

So

`y = -2x + 6`