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)#