We are given that the base AB of triangle ABC passes through the point (1,5) and divides into a ratio of 2:1. Let's call the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2).

Since AB divides into a ratio of 2:1, the coordinates of point B can be found using the following formula:

x2 = (2*x1 + x)/(2+1) = (2*x1 + 1)/3
y2 = (2*y1 + y)/(2+1) = (2*y1 + 5)/3

We know that point B passes through the point (1,5), so we can substitute these coordinates into the formulas:

x2 = (2*x1 + 1)/3 = 1
(2*x1 + 1) = 3
2*x1 = 2
x1 = 1

y2 = (2*y1 + 5)/3 = 5
(2*y1 + 5) = 15
2*y1 = 10
y1 = 5

Therefore, the coordinates of point A are (x1, y1) = (1, 5).

Now, we can find the equation of AC. Let's call the coordinates of point C as (x3, y3).

The slope of AC can be found using the formula:

slope_AC = (y3 - y1)/(x3 - x1)

Let's denote the slope of AC as m_AC.

m_AC = (y3 - 5)/(x3 - 1)

Since AB divides into a ratio of 2:1, the coordinates of point C can be found using the following formula:

x3 = (x1 + 2*x2)/3 = (1 + 2*(2*x1 + 1)/3)/3 = (1 + 2*(2*1 + 1)/3)/3 = (1 + 2*3/3)/3 = (1 + 6/3)/3 = (1 + 2)/3 = 1
y3 = (y1 + 2*y2)/3 = (5 + 2*(2*y1 + 5)/3)/3 = (5 + 2*(2*5 + 5)/3)/3 = (5 + 2*15/3)/3 = (5 + 30/3)/3 = (5 + 10)/3 = 15/3 = 5

Therefore, the coordinates of point C are (x3, y3) = (1, 5).

Now, we can substitute the coordinates of points A and C into the slope formula:

m_AC = (y3 - y1)/(x3 - x1) = (5 - 5)/(1 - 1) = 0/0

Since the slope is undefined (0/0), we cannot determine the equation of AC using the slope-intercept form or point-slope form. However, since the base AB passes through the point (1,5) and divides into a ratio of 2:1, we can determine that the line AC is a vertical line passing through the point (1,5). Therefore, the equation of AC is x = 1.