Question

What is slope in math terms?

Answer 1

In this question we have to find what is slope in Mathematics. We know that the slope of a line calculates the steepness of a line.
It is usually denoted by the letter $m$ .
It is the change in the $y$ axis by the change in the $x$ axis when we measure with respect to x-axis. These $x$ and $y$ coordinates help us to calculate the slope of the lines.

Complete step by step solution:
We know that the slope is a number that describes the direction of the line or steepness of the line. The slope is determined by finding the ratio of vertical change to the horizontal change between any two different points on a line.
We can calculate the slope with the formula of
$\dfrac{{change\,in\,y}}{{change\,in\,x}}$
This is denoted as follows;
$m = \dfrac{{\Delta y}}{{\Delta x}}$ . The small triangles are read as delta.
We should know that if $y = mx + b$ is the equation of a straight line, then $m$ is the slope and, $b$ is the $y -$ intercept.
We can see the diagram of slope from below:

Note:
We should note that the formula to calculate the slope is given by the formula:
$\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ , where $m$ is the slope of the line ,
${x_1},{x_2}$ are the coordinates of the x- axis and
${y_1},{y_2}$ are the coordinates of $y -$ axis.
Let us take an example.
We have to find the slope of the line whose coordinates are
$(2,7)$ and $(8,1)$ .
Here we have
${x_1} = 2,{x_2} = 8$ And, ${y_1} = 7,{y_2} = 1$
By putting the values in the formula we have
$m = \dfrac{{1 - 7}}{{8 - 2}}$
It gives us value
$m = \dfrac{{ - 6}}{6} = - 1$
Hence the required slope is $- 1$ .