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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

User Auino
by
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1 Answer

7 votes

Answer:


(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

User SINGULARITY
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