To find the equation of a line passing through two points, $(6, 1)$ and $(8, -1)$, we follow these steps:

Step 1: Find the slope (m)

The slope formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the values: $m = \frac{-1 - 1}{8 - 6} = \frac{-2}{2} = -1$

Step 2: Use the point-slope form

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ Using the slope $m = -1$ and one of the points, say $(6, 1)$, the equation becomes: $y - 1 = -1(x - 6)$

Step 3: Simplify the equation

Expand and simplify: $y - 1 = -x + 6$ $y = -x + 7$

Final Answer:

The equation of the line is: $y = -x + 7$

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How can you find the equation of a line in slope-intercept form using two points?
2. What is the significance of the slope in the equation of a line?
3. How can you convert an equation from point-slope form to slope-intercept form?
4. Can you find the distance between the points $(6,1)$ and $(8, -1)$?
5. What is the general form of a linear equation?

Tip: When given two points, always start by finding the slope to determine how steep the line is before proceeding with the equation.