Question

Write the equation of the line perpendicular to 2x-5y=-12 that passes through the point (10,-1) in slope-intercept form.

Answer 1

Answer:

$y=-\frac{5}{2}x-24$

Step-by-step explanation:

$2x-5y=-12\\5y=2x+12\\y=\frac{2}{5}x+\frac{12}{5}$

if two lines perpendicular,

$m_{1} .m_{2}=-1\\ \frac{2}{5} .m_{2}=-1\\m_{2}=-\frac{5}{2}$

the line perpendicular to this line is

$y=-\frac{5}{2}x+k$ ; k ∈ R

the line passes through the point (10,-1)

so,

$-1=-\frac{5}{2} (10)+k\\-1=-25+k\\k=-24$

∴the equation of the line perpendicular to 2x-5y=-12 that passes through the point (10,-1) is

$y=-\frac{5}{2}x-24$