Question

Select ALL the correct points on the graph.

If lines joined each given point on the graph to the origin, which points would be on lines that represent a unit rate less than the one represented in the table?
{(13,21) (26,42) (39,63)}
(See image attachment.)

Answer 1

the last three dots

Explanation:

Answer 2

(5, 8), (6, 7), (7, 6)

Explanation:

The table shows a rate of 21/13. This can be represented on the given graph by a line between the origin and the point (6.5, 10.5). Any point on the graph falling below that line will represent a rate less than the one in the table.

Points (5, 8), (6, 7), and (7, 6) fall below the line, so are the points you need to select.

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Comment on analytical comparison

The point (x, y) represents a unit rate of y/x. To find out if that rate is lower than 21/13, we can subtract it and see if the sign is positive.

... 21/13 - y/x = (21x -13y)/(13x)

Since we're only interested in the sign, we only need to look at the value of ...

... 21x -13y

For point (5, 8) this expression evaluates to ...

... 21·5 -13·8 = 105 -104 = 1 . . . . has a positive sign

This means the rate represented by the point (5, 8) is lower than the rate represented by the point (13, 21), so should be selected as part of the answer.