Answer:
[tex]y=-\frac{5}{2}x-24[/tex]
Step-by-step explanation:
[tex]2x-5y=-12\\5y=2x+12\\y=\frac{2}{5}x+\frac{12}{5}\\[/tex]
if two lines perpendicular,
[tex]m_{1} .m_{2}=-1\\ \frac{2}{5} .m_{2}=-1\\m_{2}=-\frac{5}{2}[/tex]
the line perpendicular to this line is
[tex]y=-\frac{5}{2}x+k[/tex] ; k ∈ R
the line passes through the point (10,-1)
so,
[tex]-1=-\frac{5}{2} (10)+k\\-1=-25+k\\k=-24[/tex]
∴the equation of the line perpendicular to 2x-5y=-12 that passes through the point (10,-1) is
[tex]y=-\frac{5}{2}x-24[/tex]
