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iragen [17]
3 years ago
8

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

Mathematics
1 answer:
katrin [286]3 years ago
3 0

Answer:

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

Step-by-step 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 = \frac{y_2 - y_1}{x_2- x_1}

Where

(x_1,y_1) = (0,0)

(x_2,y_2) = (2,1)

So;

m = \frac{y_2 - y_1}{x_2- x_1}

m = \frac{1 - 0}{2-0}

m = \frac{1}{2}

Next, we determine the line equation using:

y - y_1 = m(x -x_1)

Where

m = \frac{1}{2}

(x_1,y_1) = (0,0)

y - y_1 = m(x -x_1) becomes

y - 0 = \frac{1}{2}(x - 0)

y = \frac{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 = \frac{1}{2}x

2 = \frac{1}{2} * 4

2 = \frac{4}{2}

2=2

<em>This point is on the graph</em>

<em></em>

For (4,3)

x = 4 and y = 3

Substitute 4 for x and 3 for y in y = \frac{1}{2}x

3 = \frac{1}{2} * 4

3 = \frac{4}{2}

3 \neq 2

<em>This point is not on the graph</em>

<em></em>

For (7,2)

x = 7 and y = 2

Substitute 7 for x and 2 for y in y = \frac{1}{2}x

2 = \frac{1}{2} * 7

2 = \frac{7}{2}

2 \neq 3.5

<em></em>

<em>This point is not on the graph</em>

<em></em>

<em></em>(\frac{4}{8},\frac{2}{8})<em></em>

<em></em>x = \frac{4}{8} and<em> </em>y = \frac{2}{8}<em></em>

<em>Substitute </em>\frac{4}{8}<em> for x and </em>\frac{2}{8}<em> for y in </em>y = \frac{1}{2}x<em></em>

<em></em>\frac{2}{8} = \frac{1}{2} * \frac{4}{8}<em></em>

<em></em>\frac{2}{8} = \frac{1 * 4}{8 * 2}<em></em>

<em></em>\frac{2}{8} = \frac{4}{16}<em></em>

<em></em>\frac{1}{4} = \frac{1}{4}<em></em>

<em></em>

<em>This point is on the graph</em>

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