Final answer:
The equation of the line passing through (-1,6) and (7,-2) is y = -x + 5, found by first calculating the slope using the coordinates, then using this slope and one point to find the y-intercept in the slope-intercept form.
Step-by-step explanation:
To calculate the slope of the line passing through two points, we can use the slope formula, which is the change in y (Δy) divided by the change in x (Δx). The slope formula is m = (y2 - y1) / (x2 - x1).
In this case, the two points are (-1,6) and (7,-2). Using these coordinates:
- Δy = -2 - 6 = -8
- Δx = 7 - (-1) = 8
- Slope (m) = -8 / 8 = -1
Now, having the slope, we can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept. To find b, we can substitute the slope and the coordinates of one of the points into this formula.
Using point (-1,6):
6 = (-1)(-1) + b
b = 6 - 1
b = 5
Therefore, the equation of the line is y = -1x + 5 or y = -x + 5.