The slope of a line perpendicular to other line is the negative reciprocal of the slope.
This means, if the slope of a line is x, the slope of a perpendicular line will be:
Then , the first thing we should do is to find the slope of f(x).
To find the slope of a line that passes two points P and Q we use:
In this case, we can use P = (1, 4) and Q = (-3, 2)
Then:
Now, we know that the slope of g(x) is perpendicular to f(x) which has a slope of 1/2
The reciprocal is:
And to make it the negative, we multiply by (-1):
Thus, g(x) has a slope equal to -2