Answer:
[tex] - \frac{4}{3} [/tex]
Step-by-step explanation:
gradient formula:
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
Thus, slope of the line
[tex] = \frac{5 - 1}{1 - 4} \\ = - \frac{4}{3} [/tex]
Slope of the line that passes through the points (1,5) and (4,1) is equals to [tex]\frac{-4}{3}[/tex].
" Slope is defined as the ratio of difference of the increase in y- coordinates to the difference of increase in x- coordinates."
Formula used
Two coordinates on line
[tex]( x_{1} ,y_{1})\\\\(x_{2}, y_{2})[/tex]
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
According to the question,
Given,
Point on the line
[tex]( x_{1} ,y_{1})= ( 1,5)\\\\(x_{2}, y_{2})= ( 4,1)[/tex]
Substitute the value to get the slope of the line,
Slope = [tex]\frac{1-5}{4-1 }[/tex]
= [tex]\frac{-4}{3}[/tex]
Hence, slope of the line that passes through the points (1,5) and (4,1) is equals to [tex]\frac{-4}{3}[/tex].
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