How do I find the slope of $(1, 2, 3)$ and $(3, 4, 5)$ ?

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Answer 1 · 2017-07-20T22:41:29

See a solution process below:

Slope is defined as: $"rise"/"run"$

Calculate Run

We can first, find the run by finding the distance between the $x$ and $y$ points using the formula for distance:

$d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)$

Substituting the $x$ and $y$ points gives the run as:

$d = sqrt((color(red)(3) - color(blue)(1))^2 + (color(red)(4) - color(blue)(2))^2)$

$d = sqrt(2^2 + 2^2)$

$d = sqrt(4 + 4)$

$d = sqrt(8)$

$d = sqrt(4 * 2)$

$d = sqrt(4)sqrt(2)$

$d$ or the run is $2sqrt(2)$

Calculate Rise

In 3-dimensions the Rise is the distance between the two $z$ points:

$"rise" = 5 - 3 = 2$

Calculate Slope

$"Slope" = "rise"/"run" = 2/(2sqrt(2)) = 1/sqrt(2)$

How do I find the slope of (1, 2, 3)(1, 2, 3) and (3, 4, 5)(3, 4, 5)?