Answer:
Option B 6x-7y = -11 is correct
Step-by-step explanation:
We need to write the equation of the given line in standard form.
The points are (1/2,2) and (3,1)
The equation used is:
[tex]y-y_{1}=m(x-x_{1})[/tex]
where m is the slope.
Finding slope :
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
x₁= 1/2, y₁=2, x₂=-3, y₂=-1
Putting values:
[tex]m=\frac{-1-2}{-3-1/2} \\m=\frac{6}{7}[/tex]
Now taking point (1/2,2) and slope m = 6/7 finding equation:
[tex]y-y_{1}=m(x-x_{1})y-2=\frac{6}{7}(x-\frac{1}{2})\\ 7(y-2)=6(x-\frac{1}{2})\\7y-14=6x-3\\7y-6x=-3+14\\7y-6x= 11\\Multiply \,\,with\,\, -1\\-7y+6x=-11\\6x-7y=-11[/tex]
So, Option B 6x-7y=-11 is correct
Keywords: Standard form of the equation
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