Respuesta :
The expression of the line is:
[tex]2x+4y=20[/tex]To check which points are on the line we need to substitute the values of the x-coordinate into the x of the equation, and the y-coordinate into the y of the equation, and then check that the result is equal to 20.
Let's analyze our options:
(0,5)
The x-value is 0 and the y-values is 5. So we substitute x=0 and y=5 into the expression of the line
[tex]\begin{gathered} 2x+4y=20 \\ 2(0)+4(5)=20 \end{gathered}[/tex]Solving the operations:
[tex]\begin{gathered} 0+20=20 \\ 20=20 \end{gathered}[/tex]Since the result is 20, which matches the one from the original equation, that means that the point (0,5) is on the line.
(0,10)
We do the same process, substitute the x-value that in this case is 0, and the y value that in this case is 10, into the expression of the line and check if the result is 20:
[tex]\begin{gathered} 2x+4y=20 \\ 2(0)+4(10)=20 \\ 0+40=20 \\ 40=20 \end{gathered}[/tex]The resulting expression is not correct, because 40 is not equal to 20. Thus, (0,10) is NOT in the line.
We continue doing this for the rest of the points:
(1,2)
In this point x=1 and y=2. Substituting the values:
[tex]\begin{gathered} 2(1)+4(2)=20 \\ 2+8=20 \\ 10=20 \end{gathered}[/tex]The resulting expression is not correct because 10 is not equal to 20. Thus, (1,2) is NOT in the line.
(1,4)
The x-value is 1, and the y-value is 4, Substituting into the expression:
[tex]\begin{gathered} 2(1)+4(4)=20 \\ 2+16=20 \\ 18=20 \end{gathered}[/tex]Since 18 is not equal to 20, the expression incorrect, and (1,4) is not on the line.
(5,0)
Substituting x=5 and y=0
[tex]\begin{gathered} 2(5)+4(0)=20 \\ 10+0=20 \\ 10=20 \end{gathered}[/tex]Since 10 is not equal to 20, the resulting expression is not correct, and (5,0) is NOT on the line.
(10,0)
Substituting x=10 and y=0:
[tex]\begin{gathered} 2(10)+4(0)=20 \\ 20+0=20 \\ 20=20 \end{gathered}[/tex]The resulting expression is correct, thus, (10,0) is on the line.
Answer: (0,5) and (10,0)
