Answer:
A)
The standard from of a equation of line passing through C(3,3) and D(-3,2) is:
[tex]x-6y=-15[/tex]
B)
The standard from of a equation of line passing through E(4,3) and F(6,1) is:
[tex]x+y=7[/tex]
Step-by-step explanation:
We know that the standard form of a equation of a line is given by:
[tex]Ax+By=C[/tex]
where A,B and C are constants.
Also, we know that the equation of a line passing through two points (a,b) , (c,d) is calculated as:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
A)
C(3,3) and D(-3,2)
here we have: (a,b)=(3,3) and (c,d)=(-3,2)
Hence, the equation of line is calculated as:
[tex]y-3=\dfrac{2-3}{-3-3}\times (x-3)\\\\\\y-3=\dfrac{-1}{-6}\times (x-3)\\\\\\y-3=\dfrac{1}{6}\times (x-3)\\\\\\6(y-3)=x-3\\\\6y-18=x-3\\\\x-6y=-18+3\\\\\\x-6y=-15[/tex]
B)
E(4, 3) and F(6, 1)
here we have: (a,b)=(4,3) and (c,d)=(6,1)
Hence, the equation of line is calculated as:
[tex]y-3=\dfrac{1-3}{6-4}\times (x-4)\\\\\\y-3=\dfrac{-2}{2}\times (x-4)\\\\\\y-3=-(x-4)\\\\\\y-3=-x+4\\\\\\x+y=4+3\\\\\\x+y=7[/tex]
