Answer: [tex]3x+8y+17=0[/tex]
Step-by-step explanation:
We know that the equation of a line passing through a point (a,b) ans has slope 'm' is given by :-
[tex](y-b)=m(x-b)[/tex]
Given : Slope : [tex]m=\dfrac{-3}{8}[/tex]
Point = (5, -4)
Then, the equation of a line passing through a point (5, -4) ans has slope [tex]\dfrac{-3}{8}[/tex] is given by :-
[tex](y-(-4))=\dfrac{-3}{8}(x-5)\\\\\Rightarrow\ 8(y+4)=-3(x-5)\\\\\Rightarrow\ 8y+32=-3x+15\\\\\Rightarrow\ 3x+8y+32-15\\\\\Rightarrow\ 3x+8y+17=0\ \ [\text{In standard form}][/tex]
Therefore, the standard form of the line that contains a slope of [tex]\dfrac{-3}{8}[/tex] and passes through the point (5, -4):
[tex]3x+8y+17=0[/tex]
