Final answer:
The equation of the line passing through the points (1, -6) and (-7, 2) is y = -x - 5, with a slope (m) of -1 and a y-intercept (b) of -5.
Step-by-step explanation:
To find the equation of the line that passes through the points (1, -6) and (-7, 2), we need to calculate the slope (m) and the y-intercept (b). The slope is the change in y divided by the change in x (rise over run). So, using the points given:
Slope (m) = ∆y / ∆x = (2 - (-6)) / (-7 - 1) = 8 / -8 = -1.
With the slope known, we use one of the points to find the y-intercept (b) by plugging into the slope-intercept form (y = mx + b):
-6 = (-1)(1) + b → b = -6 + 1 = -5.
Therefore, the equation of the line is y = -x - 5.