Question

How do you calculate slope from a graph?

Answer 1

Slope is defined as the change in the vertical direction divided by change in horizontal direction of any particular graph. It is a reasonable way of measuring how steep something is whose function’s graph has been made. Therefore, we shall further understand what this means for a general graph drawn in the XY-plane.

Complete step by step answer:
If we look in an XY-plane, the change in vertical direction is going to be the change in y variable and the change in horizontal direction is going to be the change in x variable. Thus, the slope of any graph drawn in an XY-plane is given as the change in y-variable divided by the change in x variable.
A Greek letter called Delta, $\Delta$ is used to express the change in some variable or quantity mathematically. Therefore, the slope is expressed as:
Slope $=\dfrac{\Delta y}{\Delta x}$
A negative slope would mean that as x increases by a certain amount, y decreases by that same amount instead of increasing. Thus, that line is called a downward sloping line. The bigger the negative slope of a line, the faster it would y decrease with respect to the increase in x.

Note: Let us say we draw a graph of a straight-line whose slope is a constant, $m$. This means that as x increases by $m$, y also increases by $m$. Now let us say we draw a graph of a straight-line whose slope is a constant, $2m$. This means that for every x increasing by $m$, y increases by $2m$. Hence, on increasing the slope of a line, its graph becomes steeper.