A 5-foot-long board is leaning against a wall so that it meets the wall at a point $4$ feet above the floor. What is the slope of the board? the solution is $\frac{4}{3}$ or $\frac {-4}{3}$ if the ladder slopes downward I actually trying to understand how to represent it in graph or drawing it to get a proof of the answer because I can't understand why slope is $\frac{4}{3}$ it's not make sense for me
2026-03-25 23:10:13.1774480213
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what is the slope of the board?
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Please see the diagram above for the slope. It is defined as: $\text{slope m} = \dfrac{y_B - y_A}{x_B - x_A}$.
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The problem assumes that the wall is perpendicular to the floor. The board then acts as the hypotenuse of a right triangle whose leg has a length of 4 because the board touches the wall 4 feet above the ground. Using the Pythagorean Theorem, we can determine that the other leg of the right triangle has a length of 3 and thus that the board touches the floor 3 feet away from the wall. The slope is just $\frac{rise}{run}$ which is either $\frac{4}{3}$ or $\frac{-4}{3}$ depending on your perspective (the board either slopes upward to the right or downward to the right depending on whether the wall is on the left side or right side of the room).