The table and the graph below each show a different relationship between the same two variables, x and y у 300 240 100 180 5 125 120 60 6 2 8 10 7 175 How much more would the value of y be on the graph than its value in the table when x = 12? (1 point) 60 30 20 70

The table and the graph below each show a different relationship between the same two variables x and y у 300 240 100 180 5 125 120 60 6 2 8 10 7 175 How much m class=

Respuesta :

We are given the graph of a line. We notice that the line goes through the origin, therefore, the equation must be of the following form:

[tex]y=mx[/tex]

Replacing the point (4, 100) we get:

[tex]100=m(4)[/tex]

Solving for "m" by dividing by 4 to both sides:

[tex]\frac{100}{4}=m[/tex]

Solving the operation:

[tex]25=m[/tex]

Replacing the value of "m":

[tex]y=25x[/tex]

Replacing the value of x = 12:

[tex]y=25(12)[/tex]

Solving the operation:

[tex]y=300[/tex]

Now for the graph, we use the same general form:

[tex]y_2=mx[/tex]

We replace the point (2, 60) we get:

[tex]60=m(2)[/tex]

Solving for "m":

[tex]\begin{gathered} \frac{60}{2}=m \\ 30=m \end{gathered}[/tex]

Replacing the value of "m":

[tex]y_2=30x[/tex]

Replacing x = 12:

[tex]\begin{gathered} y_2=(30)(12) \\ y_2=360 \end{gathered}[/tex]

Therefore, the value of "y" is 60 more on the graph in comparison with the table.

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