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Answer:

[tex]k=-7/5[/tex]

Step-by-step explanation:

you have the point [tex]A(5,6)[/tex]

from this point we know that: [tex]x=5[/tex] and [tex]y=6[/tex]

so we must substitute this into the equation [tex]2y+kx=5[/tex], and this is how we will find which value of k makes true that the point (5,6) belongs to the graph.

So substituting [tex]x=5[/tex] and [tex]y=6[/tex]:

[tex]2y+kx=5\\2(6)+k(5)=5\\12+5k=5\\[/tex]

and we clear for the variable k:

[tex]5k=5-12\\5k=-7[/tex]

and thus, k is:

[tex]k=-7/5[/tex]

the value for k must be -7/5.

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