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# Lines

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Find the value of c such that the three points (5,5), (3,1) and (6,c) lie on the same line.

Note: Three points are on the same line if the slope of the line through any two points is always the same.

May 25, 2022

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Note that the formula for slope is: $${ \text{rise} \over \text{run}} = {{y_2 - y_1 \over x_2 - x_1}}$$

Substituting the 2 points we know, we find the slope is: $${ 5 - 1 \over 5 - 3} = {4 \over 2} = 2$$

This means that the y-coordinate for x = 6 is 2 higher than the y-coordinate when x = 5.

Can you take it from here?

May 25, 2022