Question

What is the slope of the line joining $\left( 2,12 \right)$ and $\left( 6,11 \right)$ ?

Answer 1

Here we have to find the slope of the line joining the two points given. Firstly we will write the formula for finding the slope of the line given as $m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ using two points. Then we will substitute the given point in the formula and simplify it to get our desired answer.

Complete step by step solution:
We have been given the two points of the line as follows:
$\left( 2,12 \right)$ And $\left( 6,11 \right)$
Let,
$A=\left( 2,12 \right)$
$B=\left( 6,11 \right)$
We can draw the line as follows:

Now as we know that the slope of the line is calculated by formula given:
$m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$……$\left( 1 \right)$
Where $m=$ Slope and $\left( {{x}_{1}},{{y}_{1}} \right),\left( {{x}_{2}},{{y}_{2}} \right)$ are the two points of the line.
We have the two points as $\left( 2,12 \right)$ and $\left( 6,11 \right)$ so,
$\left( {{x}_{1}},{{y}_{1}} \right)=\left( 2,12 \right)$
$\left( {{x}_{1}},{{y}_{1}} \right)=\left( 6,11 \right)$
Substitute the above value in equation (1) as follows:
$\Rightarrow m=\dfrac{11-12}{6-2}$
$\Rightarrow m=-\dfrac{1}{4}$
So we got the value as $-\dfrac{1}{4}$ .
Hence, the slope of the line joining $\left( 2,12 \right)$ and $\left( 6,11 \right)$ is $-\dfrac{1}{4}$.

Note:
A line is a one-dimensional figure which is made up of a set of points extended in the opposite direction. A line has length but has no width. In two-dimension a line is made up of two points. There are many types of line such as horizontal line, vertical line, perpendicular line and parallel line. The slope of a line measures the steepness and direction of the line. Even if we take the value of $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 6,1 \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)=\left( 2,12 \right)$ still we will get the same answer as follows:
$\Rightarrow m=\dfrac{12-11}{2-6}$
$\Rightarrow m=-\dfrac{1}{4}$
We got the same answer.
Slope can be both negative as well as positive. If slope is negative the line goes up as we move along and if the slope is positive it means the line goes down as we move along.