Final answer:
The equation of the line that is perpendicular to y = -3x - 1 and passes through the point (-3, 5) is y = 1/3x + 6.
Step-by-step explanation:
To write an equation of the line that passes through (-3,5) and is perpendicular to the line y = -3x - 1, first, we need to determine the slope of the perpendicular line.
Since the slope of the given line is -3 (as it's in the form y = mx + b where m is the slope), the slope of a line perpendicular to it will be the negative reciprocal.
Therefore, the slope of the perpendicular line will be 1/3.
Using the point-slope form of a line's equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through, our equation becomes y - 5 = 1/3(x + 3).
Simplifying this to the slope-intercept form y = mx + b gives us y = 1/3x + 6 as the final equation for the line that is perpendicular to y = -3x - 1 and passes through the point (-3, 5).