Question

How do you find the slope from a pair of points \[\left( { - 5, - 4} \right)\] and \[\left( {5,2} \right)\]?

Answer 1

Hint: To find the slope, you have to divide the difference of \[y\]-coordinates of 2 end-points on a line by the difference of \[x\]-coordinates of the same endpoints. Here, \[{x_1}\] and \[{x_2}\] are \[x\]-coordinates and \[{y_1}\] and \[{y_2}\] are \[y\] coordinates on \[x\]-axis and \[y\]-axis respectively. The slope of the line can be a positive or negative value, and the formula is given by,
Slope of the line \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\].

Complete step-by-step solution:
The slope of the line is used to calculate the steepness of the line, it is usually denoted by the letter ‘\[m\]’. It is the change in \[y\] divide by the change in \[x\], and it is given by the formula,
Slope of the line \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\].
Here given points are \[\left( { - 5, - 4} \right)\] and \[\left( {5,2} \right)\],
So by the formula, here \[{x_1} = - 5,{y_1} = - 4,{x_2} = 5,{y_2} = 2\],
Now substituting the values in the formula we get,
Slope of line \[m = \dfrac{{2 - \left( { - 4} \right)}}{{5 - \left( { - 5} \right)}}\],
Now simplifying we get,
Slope \[m = \dfrac{{2 + 4}}{{5 + 5}}\],
Now again simplifying we get,
Slope \[m = \dfrac{6}{{10}}\],
Now again simplifying the fraction we get,
Slope \[m = \dfrac{3}{5}\],
Now required slope \[m = \dfrac{3}{5}\].

\[\therefore \]The slope from a pair of points \[\left( { - 5, - 4} \right)\] and \[\left( {5,2} \right)\] is \[m = \dfrac{3}{5}\].

Note: Remember that if the slope of a line is equal to zero then it is parallel to x-axis and if the slope tends to infinity then it is perpendicular to x-axis. Also, we can remember that if the x-coordinates of the two points through which the line passes are same it must be perpendicular to the x-axis and iy y-coordinates of the two points through which the line passes are same it must be parallel to the x-axis.