Answer: [tex]2x-3y=-13[/tex]
Step-by-step explanation:
Standard form of equation of line = [tex]Ax+by=C[/tex] , where A= positive integer and B and C are integers.
The equation of a line that passes through two points (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Then, the equation of a line that passes through (1, 5) and (-2, 3) will be :-
[tex](y-5)=\dfrac{3-5}{-2-1}(x-1)[/tex]
[tex]\Rightarrow\ (y-5)=\dfrac{-2}{-3}(x-1)[/tex]
[tex]\Rightarrow\ -3(y-5)=-2(x-1)[/tex]
[tex]\Rightarrow\ -3(y)-(-3)(5)=-2(x)-(-2)(1)[/tex]
[tex]\Rightarrow\ -3y+15=-2x+2[/tex] [∵ (-)(-)=(+)]
[tex]\Rightarrow\ 2x-3y=2-15[/tex] [Add 2x on both sides and subtract 15 on sides.]
[tex]\Rightarrow\ 2x-3y=-13[/tex]
Hence, the standard form of the line that passes through (1, 5) and (-2, 3) : [tex]2x-3y=-13[/tex]
