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Determine the slope of the line joining the points $\left( {3, - 2} \right)$ and $\left( {4,5} \right)$ .

Last updated date: 20th Jun 2024
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Hint: Here we have the points given and by using the formula of the slope of the line joining the points given by $\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ and substituting the values in this formula we will get the slope of the line joining the points. And by following all these steps we will solve the problem.

Formula used:
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.

Complete step-by-step answer:
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$
Hence, the slope will be equal to $7$ .

Note: Now and then, the problem will be from the graph and we need to discover the incline. For that, we will think about the two lines which are on the chart. So the more prominent the slant is the line will be stepper. The formula we had utilized in this problem is known as the two-point form of a line condition. In the event that the condition of line resembles $\dfrac{x}{a} + \dfrac{y}{b} = 1$ , at that point this type of line's condition is named as the intercept form.