Question

What do we mean by slope of a graph? What is its physical significance

Answer 1

Let's start with the physical meaning: put a marble in the middle of a large, smooth, flat table.

If the marble does not move, the table is level, which is the opposite (in one sense) of sloped (sloped means, having a slope).

If the marble moves and falls off the table, then the table is sloped down in the direction the marble moved, and sloped up in the opposite direction from the marble’s movement.

So having a slope refers to a surface that is not level and allows gravity to move an object in the direction of gravity’s pull, which on the surface of the earth, is known as down.

The physical interpretation of mathematical slope is similar. A slope of zero is equivalent to level - no marble movement. A non-zero slope means that a line, or a tangent to a curve, has a real number value that is the ratio of the y-axis displacement divided by the X-axis displacement, commonly called the rise (since the y-axis is customarily vertical so measures vertical rise and fall) over run (since the X-axis is customarily horizontal so measures distances left to right, known as the run). A positive slope rises to the right and a negative slope rises to the left (or falls to the right).

A slope can vary in degree, from slight (a small rise over a large run) to steep (a large rise over a small run). For the mathematical purists, the numerators and denominators are absolute values for these definitions. In the physical sense, it is more difficult to walk up a steep slope than a slight slope.