Question

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

Answer 1

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:

$y=mx$

Replacing the point (4, 100) we get:

$100=m(4)$

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

$\frac{100}{4}=m$

Solving the operation:

$25=m$

Replacing the value of "m":

$y=25x$

Replacing the value of x = 12:

$y=25(12)$

Solving the operation:

$y=300$

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

$y_2=mx$

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

$60=m(2)$

Solving for "m":

$\begin{gathered} \frac{60}{2}=m \\ 30=m \end{gathered}$

Replacing the value of "m":

$y_2=30x$

Replacing x = 12:

$\begin{gathered} y_2=(30)(12) \\ y_2=360 \end{gathered}$

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