Question 174323
Since the point is (1,k) this means that {{{x=1}}} and {{{y=k}}}



{{{2y+5x=10}}} Start with the given equation



{{{2k+5(1)=10}}} Plug in {{{x=1}}} and {{{y=k}}}



{{{2k+5=10}}} Multiply



{{{2k=10-5}}} Subtract 5 from both sides



{{{2k=5}}} Subtract



{{{k=(5)/(2)}}} Divide both sides by {{{2}}} to isolate {{{k}}}.



{{{k=2.5}}} Divide.



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Answer:


So the answer is {{{k=2.5}}} 



This means that the point is (1,2.5) which looks like



{{{ drawing(500, 500, -10, 10, -10, 10,
 grid(1),
 graph( 500, 500, -10, 10, -10, 10,(10-5x)/2),
 blue(circle(1,2.5,0.1)),
 blue(circle(1,2.5,0.12)),
 blue(circle(1,2.5,0.14))

)}}} Graph of {{{2y+5x=10}}} with the point (1,2.5)