Final answer:
The equation of the line perpendicular to y = 3x - 1 and passing through (-5,2) is found to be y = -1/3x + 1/3 by utilizing the point-slope formula. The slope of the new line is the negative reciprocal of the original slope, which in this case is -1/3.
Step-by-step explanation:
To find the equation of the line that passes through the point (-5,2) and is perpendicular to the line y = 3x - 1, we first need to determine the slope of the perpendicular line. Since the slope of the given line is 3 (rise over run), the slope of the line perpendicular to it will be the negative reciprocal, which is -1/3. We use the point-slope formula to write the equation for our line:
y - y1 = m(x - x1)
Plugging in our point (-5,2) and slope -1/3, we get:
y - 2 = (-1/3)(x - (-5))
y - 2 = (-1/3)(x + 5)
Now simplifying and putting it into slope-intercept form:
y = (-1/3)x - (1/3)(5) + 2
y = (-1/3)x - 5/3 + 6/3
y = (-1/3)x + 1/3
Therefore, the correct equation of the line in slope-intercept form is option d. y = -1/3x + 1/3.