Question

The table and the graph below each show a different relationship between the same two variables, x and y:

How much more would the value of y be on the graph than its value in the table when x = 12?

150
300
450
600

Answer 1

300

Explanation:

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Answer 2

300

Explanation:

Using the table, we see that for each increase in x of 1, y increases 30. For example, from x = 4 to x = 5, it is an increase of 1 in x. The corresponding y values are 120 and 150, respectively, and that is an increase of 30. For an increase of 1 in x, y increases 30. For x to be 12, it has to increase 5 units from x = 7. That is the same as 5 increases of 1 unit in x. That corresponds to 5 increases of 30 in y. 5 * 30 = 150. When x increases 5, y increases 150.

We have x = 7, y = 210.

Add 5 to x and 150 to y:

For the table, x = 12; y = 360

Now we look at the graph.

Look at (0, 0) and (2, 110) on the graph. When x increases 2 (from 0 to 2), y increases 110 (from 0 to 110). Now look at the last point on the graph. It is (8, 440). We want the y-value for x = 12. Start with x = 8, y = 440. Add 2 to x and 110 to y: (10, 550). That gives us the y value for x = 10. We need the y value for x = 12. Again, add 2 to x and 110 to y. You get (12, 660).

For the graph, x = 12; y = 660

For x = 12, the graph's y value is 660, and the table's y value is 360.

To find how much more the graph value is than the table value, we subtract:

660 - 360 = 300

Answer: 300