Question 1202856
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line containing the centers of the two circles whose equations are given below. (x-6)^2+(y-3)^2=49 (x+4)^2+(y-4)^2=81
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Say better this way:

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line containing the centers of the two circles whose equations are given below. (x-6)^2+(y-3)^2=49, AND  (x+4)^2+(y-4)^2=81
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The two points are  (6, 3)  and (-4, 4).
IF you already know how to find equation of a line through two given points, then you're all set knowing what to do.


Do you understand why this is or can be used?    {{{y-3=-(1/10)(x-6)}}}



In more detail,

Picking the point  (6, 3) as build the variable slope expression
and both points for the slope value
{{{(y-3)/(x-6)=(4-3)/(-4-6)}}}

{{{(y-3)/(x-6)=1/(-10)}}}

{{{(y-3)/(x-6)=-1/10}}}

{{{y-3=-(1/10)(x-6)}}}

{{{y-3=-x/10+6/10}}}

{{{y=-x/10+3/5+3}}}

{{{highlight(y=-x/10+3&3/5)}}}