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If we have a point given as $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ then the slope of the line joining the points will be given by

$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$

Here, $m$ will be the slope of a line.

So we have the points given as $\left( {3, - 2} \right)$ and $\left( {4,5} \right)$ . So on comparing with $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ we will have the respective position of the points.

So by using the formula for the slope of a line, we get

$ \Rightarrow m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$

Now on substituting the values, in the above equation, we get the slope as

$ \Rightarrow m = \dfrac{{5 + 2}}{{4 - 3}}$

And on solving the numerator and the denominator of the given function, we get the equation as

$ \Rightarrow m = \dfrac{7}{1}$

Therefore, the above fraction of the slope can be written as

$ \Rightarrow m = 1$

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