Respuesta :
Line v passes through points (1, 12) and (10, 7). The slope of line w as improper fraction is [tex]\frac{9}{5}[/tex]
Solution:
Given, two points are (1, 12) and (10, 7)
We have to find the slope of a line that is perpendicular to line passing through the above given two points.
Slope of a line that pass through [tex]\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)[/tex] is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\text { Here, in our problem, } x_{1}=1, y_{1}=12 \text { and } x_{2}=10, y_{2}=7[/tex]
[tex]\text { slope } m=\frac{7-12}{10-1}=\frac{-5}{9}[/tex]
So, slope of line v is [tex]\frac{-5}{9}[/tex]
Since line w is perpendicular to v, the product of their slopes equals -1
[tex]\text { slope line } v \times \text { slope of line } w=-1[/tex]
[tex]\frac{-5}{9} \times \text { slope of line } w=-1[/tex]
[tex]\text { Slope of line } w=\frac{9}{-5} \times(-1)=\frac{9}{5}[/tex]
Hence, the slope of line w as improper fraction is [tex]\frac{9}{5}[/tex]
