Question

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

Answer 1

ANSWER

EXPLANATION

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

$\begin{gathered} 2x\text{ - 5y = 5} \\ -5y\text{ = 5 - 2x} \\ \text{Divide through by -5:} \\ y\text{ = }\frac{5}{-5}\text{ - }\frac{2x}{-5} \\ y\text{ = }\frac{2}{5}x\text{ - 1} \end{gathered}$

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:

$\begin{gathered} -\frac{1}{\frac{2}{5}} \\ =\text{ -}\frac{5}{2} \end{gathered}$