Question

Two collinear points on a line are given in the table below:

X y

0 0 (0,0)
2 1 (2,1)

Select the points that do not lie on the line.

(4,2)
(4, 3)
(7,2)
4/8, 2/8

Answer 1

`(4,3)` and
`(7,2)` do not lie on the line

Explanation:

Given

`(0,0)\ and\ (2,1)`

Required

Determine which points that are not on the line

First, we need to determine the slope (m) of the line:

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

Where

`(x_1,y_1) = (0,0)`

`(x_2,y_2) = (2,1)`

So;

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

`m = (1 - 0)/(2-0)`

`m = (1)/(2)`

Next, we determine the line equation using:

`y - y_1 = m(x -x_1)`

Where

`m = (1)/(2)`

`(x_1,y_1) = (0,0)`

`y - y_1 = m(x -x_1)` becomes

`y - 0 = (1)/(2)(x - 0)`

`y = (1)/(2)x`

To determine which point is on the line, we simply plug in the values of x to in the equation check.

For
`(4,2)`

`x = 4` and
`y =2`

Substitute 4 for x and 2 for y in
`y = (1)/(2)x`

`2 = (1)/(2) * 4`

`2 = (4)/(2)`

`2=2`

This point is on the graph

For
`(4,3)`

`x = 4` and
`y = 3`

Substitute 4 for x and 3 for y in
`y = (1)/(2)x`

`3 = (1)/(2) * 4`

`3 = (4)/(2)`

`3 \\eq 2`

This point is not on the graph

For
`(7,2)`

`x = 7` and
`y = 2`

Substitute 7 for x and 2 for y in
`y = (1)/(2)x`

`2 = (1)/(2) * 7`

`2 = (7)/(2)`

`2 \\eq 3.5`

This point is not on the graph

`((4)/(8),(2)/(8))`

`x = (4)/(8)` and
`y = (2)/(8)`

Substitute
`(4)/(8)` for x and
`(2)/(8)` for y in
`y = (1)/(2)x`

`(2)/(8) = (1)/(2) * (4)/(8)`

`(2)/(8) = (1 * 4)/(8 * 2)`

`(2)/(8) = (4)/(16)`

`(1)/(4) = (1)/(4)`

This point is on the graph