You have slope and a point so it should be easy.
Set up equation [y-y1= m(x-x1)]
y-5 = -5/6(x-6)
And simplify.
Y=-5/6x +10
Then to find x intercept, plug in a 0 for y
0=-5/6x+10
-10=-5/6x. Subtract 10 from both sides.
-10/ -5/6 = x. Divide by -5/6 on both sides.
X=12
So the x intercept is 12 or (12,0)