Answer :
Answer:
5x-2y=23
Step-by-step explanation:
The line is passing through the points (3,-4) and (5,1).
Thus, we have
[tex]x_1=3,y_1=-4,x_2=5,y_2=1[/tex]
The slope of the line is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1+4}{5-3}\\\\m=\frac{5}{2}[/tex]
The point slope form of a line is given by
[tex]y-y_1=m(x-x_1)\\\\y+4=\frac{5}{2}(x-3)\\\\y+4=\frac{5}{2}x-\frac{15}{2}\\\\2y+8=5x-15\\\\5x-2y=23[/tex]
Thus, the standard form of the line is given by 5x-2y=23
Answer: [tex]5x-2y=23[/tex]
Step-by-step explanation:
The equation of a line passing through (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Also , the equation of a line in standard form is given by :-
[tex]Ax+By=C[/tex]
Then , the equation of a line passing through points (3,-4) and (5,1) will be :-
[tex](y-1)=\dfrac{-4-1}{3-5}(x-5)[/tex]
[tex]\Rightarrow\ (y-1)=\dfrac{-5}{-2}(x-5)[/tex]
[tex]\Rightarrow\ (y-1)=\dfrac{5}{2}(x-5)[/tex]
Convert into standard form.
[tex]\Rightarrow\ 2(y-1)=5(x-5)[/tex]
[tex]\Rightarrow\ 2y-2=5x-25[/tex]
[tex]\Rightarrow\ 25-2=5x-2y[/tex]
[tex]\Rightarrow\ 5x-2y=23[/tex]
Hence, the standard form of the line passing through the points (3,-4) and (5,1) : [tex]5x-2y=23[/tex]