Final answer:
The linear equation of a line parallel to y = -2/3x + 1 and passing through (-6, -1) is y = -2/3x - 5.
Step-by-step explanation:
To find the linear equation of a line parallel to y = -2/3x + 1 and passing through the point (-6, -1), we can use the concept that parallel lines have the same slope. Since the given line has a slope of -2/3, our new line must also have this slope. The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
To find b, we can plug in the coordinates of the point the line passes through:
- y = -1 when x = -6
- -1 = (-2/3)(-6) + b
- -1 = 4 + b
- b = -5
Therefore, the equation of our line is y = -2/3x - 5.