Question

Select all the correct points on the graph. if lines jointed each given point of the graph to the origin, which points would it be on the lines that represent the unit rate less than one represented in the table?

Answer 1

The first step is to determine the unit rate represented on the table.

If x and y have a direct relationship then

`y=kx`

k represents the coefficient of variation (or unit rate)

k can be calculated as

`k=(y)/(x)`

To determine the unit rate represented on the table use a set of values, for example (13, 21)

`k=(21)/(13)\cong1.615`

Now you have to determine the unit rate for each point on the graph and compare to the unit rate represented on the table.

Purple point

Coordinates (2,8)

Unit rate

`k=(8)/(2)=4`

The unit rate is greater than the one expressed on the table.

Red point

Coordinates (3,9)

Unit rate

`k=(9)/(3)=3`

The unit rate is greater than the one expressed on the table.

Blue point

Coordinates (4, 10)

Unit rate

`k=(10)/(4)=(5)/(2)\cong2.5`

The unit rate is greater than the one expressed on the table.

Green point

Coordinates (5, 8)

Unit rate

`k=(8)/(5)=1.6`

The unit rate is less than the one represented in the table by 0.005

Brown point

Coordinates (6, 7)

Unit rate

`k=(7)/(6)=1.167`

The unit rate is less than the one represented in the table.

Dark blue point

Coordinates (7, 6)

Unit rate

`k=(6)/(7)\cong0.857`

The unit rate is less than the one represented in the table.

The green (5,8), brown (6,7) and dark blue (7,6) points have a unit rate less than the one represented on the table.