Question 485956
A straight line has the equation {{{y=m*x+c}}} where the slope of the line is m and c is where the line crosses the y axis.

You have 2 solutions to this equation (1/6,1/3) and (5/6,1) so put these values in the straight line equation...
the first (x,y) coordinate gives you {{{1/3=m*(1/6)+c}}}
the second leads to {{{1=m*(5/6)+c}}}

This is a simple simultaneous equation to find m and c.

Subtracting these 2 equations gives {{{(1/3-1)=m*(1/6-5/6)+(c-c)}}}
so {{{-2/3=m*(-2/3)}}} which gives m=1

now put m=1 into either the equations to find c, for example
{{{1/3=1*(1/6)+c}}} and then it is easy to show {{{c=1/6}}}

so the equation for the line is {{{y=x+1/6}}}