Answer: [tex]x+4y+4=0[[/tex]
Step-by-step explanation:
The point-slope form of a line that passes from point (a,b) has slope m is given by :-
[tex](y-b)=m(x-a)[/tex]
Then , the point-slope form of a line that passes from point (8, –3) and has slope [tex]m=\dfrac{-1}{4}[/tex] is given by :-
[tex](y-(-3))=\dfrac{-1}{4)}(x-8)\\\\ 4(y+3)=-1(x-8)\\\\ 4y+12=8-x\\\\ x+4y+4=0[/tex]
Hence, the equation in point-slope form for the line through the given point (8, –3) with the given slope [tex]m=\dfrac{-1}{4}[/tex] is [tex]x+4y+4=0[[/tex]
