5, 6) and (7, 7)

To find the equation of a line passing through the points (5, 6) and (7, 7), we can use the slope-intercept form of a linear equation, which is y = mx + b.

First, let's find the slope (m) of the line using the formula:

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

Let (x1, y1) = (5, 6) and (x2, y2) = (7, 7).

m = (7 - 6) / (7 - 5) = 1 / 2 = 0.5

So the slope of the line is 0.5.

Now, let's find the value of b by substituting one of the given points into the slope-intercept form:

y = mx + b
6 = 0.5 * 5 + b
6 = 2.5 + b
b = 6 - 2.5
b = 3.5

Therefore, the equation of the line passing through the points (5, 6) and (7, 7) is y = 0.5x + 3.5.