[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-7-6}{-5-1}\implies \cfrac{-13}{-6}\implies \cfrac{13}{6}[/tex]
The slope of the line is [tex]\frac{13}{6}[/tex].
A slope of a line is the change in y coordinate with respect to the change in x coordinate.
If [tex]P(x_{1} ,y_{1} )[/tex] and [tex]Q(x_{2} ,y_{2} )[/tex] are the two points on a straight line, then the slope formula is given by:
Slope, m = Change in y-coordinates/Change in x-coordinates
[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
According to the given question.
We have a two points (1, 6) and (-5,-7).
Therefore, the slope of the line from these points is given by
[tex]slope = \frac{-7-6}{-5-1} = \frac{-13}{-6} =\frac{13}{6}[/tex]
Hence, the slope of the line is [tex]\frac{13}{6}[/tex].
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