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How do you find the slope of the line passing through each pair of points. $\left( -3,-1 \right),\left( -1,5 \right)?$

Last updated date: 14th Jul 2024
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Hint: Slope is the change in the $y$-value divided by the change in the $x$-values.
Slope $=\dfrac{\text{Rate of change }my}{\text{Rate of change }mx}=\dfrac{rise}{sun}$
It is often expressed as rise over run. Identify $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ from given question.

Complete step by step solution:
As per the given problem, $\left( -3,-1 \right)$ and $\left( -1,5 \right)$ we the two points passing through the slope.
So, here you have to identify $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ from the given points.
Therefore, $\left( -3,-1 \right)$ and $\left( -1,5 \right)$
Because points are written in $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ form.
Here, formula for finding the slope of the line passing two points is.
Slope of line $\left( m \right)=\dfrac{Rise}{Run}$
$=\dfrac{\text{Rate of change in value of }y}{\text{Rate of change in value of }x}$
Slope of the line $\left( m \right)=3$
Hence slope of line passing through each pair of points $\left( -3,-1 \right)$and $\left( -1,5 \right)$ is $3.$

Additional Information:
The slope is a number that tells how much $'y'$ changes when $'x'$ changes. For example: a slope of $5$ means that for each change in $x$ of $1$ unit (for example between $6$ and $7)$ the corresponding $y$ changes of $5$units. This is for a positive slope, so that your value of $y$ is getting bigger.
The negative slope is the opposite. It tells you of how much $y$ decreases for each in orase of $1$ unit in $x.$ A slope of $-5$ tells you that the value of $y$-decreases of $5.$ units in the $1$unit interval of $x.$
Remember the slope of line is defined as
And the rise of the horizontal line is zero since it is neither increasing nor decreasing. Therefore the slope of the line is zero.

Apply the formula of slope of line $m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
Where, ${{x}_{2}},{{x}_{1}}$ are the $x$ component of a given pair. And ${{y}_{1}},{{y}_{2}}$ are the $y$ components of a given pair.
Always remember that as in the formula $'-{{y}_{1}}'$ is given and if the value of $'{{y}_{1}}'$ is $'-1'$
Therefore it will become $+1$
$'-'\times '-'='+'$