Answer
The slope of a line is the rate of increase of its y coordinate with respect to the x coordinate. It is calculated by the formula shown below:
$m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
Work Step by Step
The slope of a line can be defined as the ratio of the vertical change to the horizontal change when moving from one fixed point to another along a line.
It compares the rise to the run while moving along the line.
The slope of a line is calculated using two points. The formula for the slope of a line passing through the distinct points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is as follows:
$m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
Example:
Consider a line that passes through the given points $\left( 3,-2 \right)$ and $\left( 1,4 \right)$.
The slope of a line passing through the points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is as follows:
$m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
Substitute $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 3,-2 \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)=\left( 1,4 \right)$; the slope of the line is:
$\begin{align}
& m=\frac{4-\left( -2 \right)}{1-3} \\
& =\frac{4+2}{\left( -2 \right)} \\
& =\frac{6}{\left( -2 \right)} \\
& =-3
\end{align}$
Thus, the slope of the given line is $m=-3$.
Positive slope indicates that the line will rise from left to right and negative slope indicates that the line will fall from left to right.
The slope of this line is negative so it falls from left to right.
