Question

How is the slope of a line related to speed?

Answer 1

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. Or it is a change in $y$ over the change in $x$. Speed can be thought of as the rate at which an object covers distance. It is a scalar quantity; it means it has only magnitude but no direction.

Complete step by step solution:
We know that the formula of finding the speed is:
$\Rightarrow s=\dfrac{d}{t}$, where $d$ is the distance travelled by the object, and $t$ is the time taken by that object. And it is clear by the above formula of the speed that $d$ is a function of $t$, which can be written as:
$\Rightarrow d=st$
This above equation indicates that if the time and speed increases, the distance travelled by object also increases.
We know that the general formula for the slope-intercept form is $y=mx+b$. In this intercept form we can easily see here the $y$ is also the function of $x$.
Now we can easily notice that our function $d$ and $y$ are both are similar to each other, that means the function $d$ is written in the slope-intercept form, we can write it as$\Rightarrow d=st+b$, where $b$ is equals to zero, that is,
$\Rightarrow d=st+0$
Hence the speed is the slope of the function expressing distance as a function of time.

Note: The minor difference between speed and slope is the slope has direction but speed has no direction but still slope of the line is related to the speed because the intercept of speed is zero.