Final answer:
The slope of the line passing through the points (2,6) and (6,4) is -0.5, indicating a descending line from left to right.
Step-by-step explanation:
To calculate the slope of a line that passes through the points (2,6) and (6,4), we use the formula for slope, which is the change in y-coordinates divided by the change in x-coordinates. This is often referred to as 'rise over run'.
First, identify the coordinates of the two points: Point 1 (x1, y1) = (2, 6) and Point 2 (x2, y2) = (6, 4).
- Subtract the y-coordinate of Point 1 from the y-coordinate of Point 2 to find the rise: 4 - 6 = -2.
- Subtract the x-coordinate of Point 1 from the x-coordinate of Point 2 to find the run: 6 - 2 = 4.
- Divide the rise by the run to find the slope: -2 / 4 = -0.5.
The slope of the line is -0.5, indicating that for every unit increase in x, the y-value decreases by 0.5 units. The line is descending from left to right.
With the calculated slope, we can determine the line's direction and form an equation if needed.