We have to find the slope of a line that is perpendicular to a line with slope 3/4.
Perpendicular lines have slopes that are negative reciprocals. Then, if m1 and m2 are the slopes of two perpendicular lines, we will have:
[tex]m_1=-\frac{1}{m_2}[/tex]Then, if one of our lines has a slope of 3/4, perpendicular lines will have a slope m as:
[tex]m=\frac{1}{-(\frac{3}{4})}=-\frac{4}{3}[/tex]Answer: the slope of a perpendicular line will be -4/3.
