The slopes of perpendicular lines are opposite reciprocals.
For the given function:
[tex]5y=-6x+2[/tex]Solve y to identify the slope (y=mx+b, m is the slope)
[tex]\begin{gathered} y=-\frac{6}{5}x+\frac{2}{5} \\ \\ \text{Slope:} \\ m=-\frac{6}{5} \\ \\ \text{Slope of perpendicular line:} \\ -\frac{1}{m} \\ \\ -\frac{1}{-\frac{6}{5}}=\frac{5}{6} \\ \\ \end{gathered}[/tex]The slope of the perpendicular line to the given function is 5/6. For the given options the equation with slope 5/6 is: B. 6y=5x+3
[tex]\begin{gathered} 6y=5x+3 \\ \\ y=\frac{5}{6}x+\frac{3}{6} \\ \\ \text{slope: }\frac{5}{6} \end{gathered}[/tex]
