Answer: [tex]y=-5x+21[/tex]
Step-by-step explanation:
In slope intercept form : y=mx+c , m= slope , c= y-intercept.
Let [tex]L_1[/tex] be the line passing through (5, -4) and perpendicular to [tex]L_2: 2x-10y=0[/tex].
Rewrite [tex]L_2[/tex] in slope-intercept form
[tex]10y=2x\Rightarrow\ y=0.2x+0[/tex]
Here, Slope of [tex]L_2[/tex] = m = 0.2
Let n be slope of [tex]L_1[/tex] .
Then [tex]m\times n=-1[/tex] [Product of slopes of perpendicular lines is -1.]
[tex]\Rightarrow\ n=\dfrac{-1}{m}=\dfrac{-1}{0.2}\\\\\Rightarrow\ n=-5[/tex]
Equation of a line that passes through (a,b) and have slope 'm' is given by :-
[tex](y-b)=m(x-a)[/tex]
So, Equation of [tex]L_1[/tex] :
[tex](y-(-4))=-5(x-5)\\\\\Rightarrow\ (y+4)=-5x+25\\\\\Rightarrow\ y=-5x+21[/tex]
