Question

What is the equation of a perpendicular to the line with equation 2x-5y=5

Answer 1

Step-by-step explanation

First, let us put the equation in slope intercept form:

`\begin{gathered} 2x\text{ - 5y = 5} \\ -5y\text{ = 5 - 2x} \\ \text{Divide through by -5:} \\ y\text{ = }(5)/(-5)\text{ - }(2x)/(-5) \\ y\text{ = }(2)/(5)x\text{ - 1} \end{gathered}`

where slope = 2/5

intercept = -1

The equation of a line perpendicular to this line has a slope that is the negative inverse of the given line.

So, we have to find the negative inverse of 2/5

That is:

`\begin{gathered} -(1)/((2)/(5)) \\ =\text{ -}(5)/(2) \end{gathered}`