Question

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

Answer 1

Answer:

$k =6$

Step-by-step explanation:

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

Answer 2

Answer:

k = 6

Step-by-step 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 = - $\frac{1}{k}$ x + $\frac{18}{k}$ ← in slope- intercept form

with slope m = - $\frac{1}{k}$

given m = - $\frac{1}{6}$ , then equating

- $\frac{1}{k}$ = - $\frac{1}{6}$ ⇒ k = 6