Question

If we draw lines to join each given point to the origin, identify the points whose corresponding line has a slope that is an integer value.

Answer 1

Brown circle red circle and blue circle

Explanation:

Answer 2

The slopes of OA, OB ans OC are integer values.

Explanation:

If a line passing through two points then the slope of the line is

`m=(y_2-y_1)/(x_2-x_1)`

If one point is origin then the slope of the line is

`m=(y_2-0)/(x_2-0)=(y_2)/(x_2)`

The slope of line OA is

`m_(OA)=(8)/(2)=4`

It is an integer.

The slope of line OB is

`m_(OB)=(9)/(3)=3`

It is an integer.

The slope of line OC is

`m_(OC)=(8)/(4)=2`

It is an integer.

The slope of line OD is

`m_(OD)=(8)/(5)`

It is not an integer.

The slope of line OE is

`m_(OE)=(7)/(6)`

It is not an integer.

The slope of line OF is

`m_(OF)=(6)/(7)`

It is not an integer.

Therefore the slopes of OA, OB ans OC are integer values.