Answer:
y = (1/3)x + 7
Explanation:
The slope of a line perpendicular to the given line y = -3x - 2 would have to be the negative reciprocal of the slope of the given line:
or, in other words,
the negative reciprocal of -3. That would be +1/3.
Starting with the slope-intercept form of the equation of a straight line, we have:
y = mx + b.
We substitute the coordinates of the given point, (-9,4), and the slope +1/3:
4 = (1/3)(-9) + b.
This simplifies to
4 = -3 + b, from which it can be easily seen that b = 7.
The desired line is y = (1/3)x + 7.