two lines are perpendicular when the multiplication of their slopes is equal to -1. The slope of y = 3x - 4 is 3. Then the slope of a perpendicular line is:
[tex]\begin{gathered} m\cdot3=-1 \\ m=-\frac{1}{3} \end{gathered}[/tex]Slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. Replacing with point (-3, 5) and m = -1/3, we get:
5 = -1/3(-3) + b
5 = 1+ b
5 - 1 = b
4 = b
Then, the equation is:
y = -1/3x + 4
