Final answer:
The equation of the line passing through the points (1, -15) and (-6, -1) is y = -2x - 13.
Step-by-step explanation:
To find the equation of a line passing through two points, we can use the formula for the slope (m) of the line, which is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. After calculating the slope, we can use the point-slope form of a line's equation, which is y - y1 = m(x - x1), to find the specific equation of our line.
Now, let's calculate the slope using the points (1, -15) and (-6, -1). The slope m would be:
m = (-1 + 15) / (-6 - 1) = 14 / -7 = -2
Now, using the point-slope form with point (1, -15) and slope m = -2, we get:
y - (-15) = -2(x - 1)
Our equation of the line is:
y + 15 = -2x + 2
After further simplifying:
y = -2x - 13
This is the final equation of the line.