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 = - [tex]\frac{1}{k}[/tex] x + [tex]\frac{18}{k}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{1}{k}[/tex]
given m = - [tex]\frac{1}{6}[/tex] , then equating
- [tex]\frac{1}{k}[/tex] = - [tex]\frac{1}{6}[/tex] ⇒ k = 6
Answer:
[tex]k =6[/tex]
Step-by-step explanation:
[tex]~~~~~~~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[/tex]
