To find the equation of the line that passes through the points $(25, 26)$ and $(8, 9)$, we can use the two-point form of the equation of a line.

Step 1: Find the slope (m) using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$ Here, $(x_1, y_1) = (25, 26)$ and $(x_2, y_2) = (8, 9)$.

$m = \frac{9 - 26}{8 - 25} = \frac{-17}{-17} = 1$

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

$y - y_1 = m(x - x_1)$ Substitute $m = 1$ and the coordinates of one of the points (say, $(25, 26)$):

$y - 26 = 1(x - 25)$

Step 3: Simplify the equation:

$y - 26 = x - 25$

$y = x + 1$

Final Equation:

The equation of the line is: $y = x + 1$

Do you need any further explanation or details?

Here are 5 related questions to expand on this topic:

1. How do you find the equation of a line using the slope-intercept form?
2. What happens if the slope of a line is zero? How would the equation change?
3. Can you find the equation of a line parallel to this one that passes through a given point?
4. What are the properties of perpendicular lines, and how do their slopes relate?
5. How can you convert a line equation from point-slope form to standard form?

Tip: Always check the slope first, as it helps determine the direction and steepness of the line.