If two lines are perpendicular, then their slopes have a product of -1 or you could say they are opposite signed reciprocals of each other.
The given equation has a slope of -3. We know this because it is in slope-intercept form y = mx + b ...y = (slope)x + (y-intercept).
so taking the slope -3...the opposite signed reciprocal would be +\(\frac{1}{3}\)
Now we have a slope and a point... we can use them to find the b (y-intercept)
x = 4, y = 3, and m = \(\frac{1}{3}\)
\(3= \frac{1}{3} (4)+b\)
\(3= \frac{4}{3} +b\)
Using the common denominator fraction for 3, we subtract 4/3 from both sides
\(3= \frac{9}{3}\)
\(\frac{5}{3} =b\)
plug the values for m and b into the slope intercept form
\(y= \frac{1}{3} x+ \frac{5}{3}\)