Question

The line x +ky=18 has a gradient of - 1/6 (a) Find the value of k.​

Answer 1

`k =6`

Explanation:

`~~~~~~~x+ky = 18\\\\\implies ky = -x +18\\\\\implies y = -\frac 1k x+ \frac{18}k\\\\\text{It is now in the slope intercept form (y=mx +c), where m is the slope.}\\\\\text{Given that,}\\\\~~~~~m = -\frac 16\\\\\implies -\frac 1k = -\frac 16\\\\\implies \frac 1k = \frac 16\\\\\implies k =6`

Answer 2

k = 6

Explanation:

the equation of a line in slope- intercept form is

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

given

x + ky = 18 ( subtract x from both sides )

ky = - x + 18 ( divide through by k )

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

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

given m = -
`(1)/(6)` , then equating

-
`(1)/(k)` = -
`(1)/(6)` ⇒ k = 6