Question 1089601
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Make a sketch.

Find and draw a right angled triangle in your sketch.


(1 + 4) = 5 is the length of the hypotenuse of the right-angled triangle.

(4 - 1) = 3 is the length of the vertical leg.

You need to find the length of the horizontal leg.


The slope is {{{delta_y/delta_x}}} = {{{(4-1)/sqrt((1 + 4)^2-(4-1)^2))}}} = {{{3/sqrt(5^2 - 3^2)}}} = {{{3/sqrt(25-9)}}} = {{{3/sqrt(16)}}} = {{{3/4}}}.
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Solved.