Given the line equation
[tex]2x-5y=7[/tex]Let's consider a generic line with coefficients
[tex]ax+by=c[/tex]The perpendicular line will be
[tex]bx-ay=d_{}[/tex]Fact, we just need to change the coefficients and the ONLY one signal. Then, again, given
[tex]2x-5y=7[/tex]We need to change the x and y coefficient:
[tex]5x-2y=c[/tex]Now we change the signal of the coefficient with "y"
[tex]5x+2y=c[/tex]The value of c here doesn't matter, just the coefficients, then, the final answer is
[tex]5x+2y=3[/tex]That's the line equation perpendicular to the line 2x – 5y = 7