Final answer:
The correct equation of the line perpendicular to y = 3x and passing through (-2, 2) is y = -x + 4. This is found by taking the negative reciprocal of the given slope and then solving for the y-intercept using the given point.
Step-by-step explanation:
To find the slope-intercept form of a line that is perpendicular to another line, we must first understand that perpendicular lines have slopes that are negative reciprocals of one another. Given the equation y = 3x, we know the slope of this line is 3. Therefore, the slope of the line perpendicular to it would be -1/3 (the negative reciprocal).
Next, we use the point given, (-2, 2), and the slope -1/3 to plug into the slope-intercept form equation y = mx + b, where m is the slope and b is the y-intercept. We can substitute the coordinates of the point into the equation as such:
2 = (-1/3)(-2) + b
2 = 2/3 + b
Subtract 2/3 from both sides to solve for b:
b = 2 - 2/3
b = 6/3 - 2/3
b = 4/3
The equation of the line is therefore y = (-1/3)x + 4/3. None of the given choices match this equation precisely, but you may need to multiply the entire equation by 3 to get rid of the fraction. Doing so gives y = -x + 4, which is the correct choice B.