Question

Question #4d894

Answer 1

`k = (-10)/3`

Explanation:

Rearranging `3x + 2y - 5 = 0` to fit the form `y = mx + c`:

`2y = -3x + 5`

`(2y)/2 = (-3x + 5)/2`

`y =(-3)/2x + 5/2`

So `m_1 = (-3)/2`

Rearranging `kx - 5y + 8 = 0` to fit the form `y = mx + c`:

`-5y = -kx - 8`

`5y = kx + 8`

`(5y)/5 = (kx + 8)/5`

`y = k/5x + 8/5`

So `m_2 = k/5`

If the lines are perpendicular then we know that the gradients must be opposites of each other (`m_2= -1/(m_1)`)

So:

`k/5= -1/((-3)/2)`
`k/5= (-2)/3`
`k = (-10)/3`

Answer 2

The slope of the straight line
`3x + 2y - 5= 0 or y = -3/2x+5/2=0` is `m_1=-3/2`.

Again the slope of the straight line
`kx -5y +8= 0 or y = k/5x+8/5=0` is `m_2=k/5`.

As the straight lines are perpendicular to each other then

`m_1xxm_2=-1`

`=>-3/2xxk/5=-1`

`=>k=10/3`