Question

Write an equation of a line that would be perpendicular to 2x-5y=10

Answer 1

We want to write the equation of a line that is perpendicular to:

`2x-5y=10`

We remember that two perpendicular lines have opposite inverse slopes. This means that when we multiply the slopes of the two lines, we obtain -1. Thus, we will find the slope of the equation given by solving for y:

`\begin{gathered} 2x-5y-2x=10-2x \\ 0-5y=10-2x \\ -5y=10-2x \\ y=(10-2x)/(-5) \\ y=-2+(2)/(5)x \end{gathered}`

This means that the slope of the line given is 2/5. For finding a opposite inverse number to the one given, we interchange the numerator and the denominator, and we change its sign:

Thus, the slope of the perpendicular line should be:

`-(5)/(2)`

And we can choose its y-intercept. On this case, we will choose the y-intercept to be 0, and we get that an equation of a line that is perpendicular to 2x-5y=10 is:

`\begin{gathered} y=-(5)/(2)x \\ \text{ Or, equivalently:} \\ 5x+2y=0 \end{gathered}`