The function g(x) has a slope of -5/6. The value of g(x) is 5 when x is 6. Explain how the graph of g (x) can be used to find the x-intercept.
You are given the slope and a point on the line.
That is sufficient condition to find its equation:
g(6) = 5 tells you (6,5) is your point, using the point-slope method:
y - 5 = (-5/6)(x-6)
multiply by 6
6y - 30 = -5(x - 6)
6y - 30 = -5x + 30
5x + 6y = 60 is our equation
to find the x-intercept, we let y = 0 and solve for x
looks like x = 12 is our x-intercept