The equation of the line joining the points (2,5) and (5,11) is:

Step 1: Find the slope of the line

The slope of the line (m) passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the given points (2,5) and (5,11) into the formula, we get:

m = (11 - 5) / (5 - 2) = 6 / 3 = 2

Step 2: Use the point-slope form of the line equation

The point-slope form of the line equation is:

y - y1 = m(x - x1)

Substituting the slope we found and one of the given points into the equation, we get:

y - 5 = 2(x - 2)

Step 3: Simplify the equation

Distribute the 2 on the right side of the equation:

y - 5 = 2x - 4

Then, add 5 to both sides to solve for y:

y = 2x + 1

So, the equation of the line joining the points (2,5) and (5,11) is y = 2x + 1.