Question

32. Which of these lines is perpendicular to the line 5y = -6x + 2?A. 6y = -5x + 3B. 6y = 5x + 3C. 5y = -6x + 8D. 5y = 6x + 8

Answer 1

The slopes of perpendicular lines are opposite reciprocals.

For the given function:

`5y=-6x+2`

Solve y to identify the slope (y=mx+b, m is the slope)

`\begin{gathered} y=-(6)/(5)x+(2)/(5) \\ \\ \text{Slope:} \\ m=-(6)/(5) \\ \\ \text{Slope of perpendicular line:} \\ -(1)/(m) \\ \\ -(1)/(-(6)/(5))=(5)/(6) \\ \\ \end{gathered}`

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

`\begin{gathered} 6y=5x+3 \\ \\ y=(5)/(6)x+(3)/(6) \\ \\ \text{slope: }(5)/(6) \end{gathered}`