The point slope form of (-5, 4) and (5, 1) is [tex]y-4=\frac{-3}{5}(x+5)[/tex]
Solution:
Given that a line is passing through points (-5,4) and (5,1)
We need to determine point slope form of line
Equation of line passing through point [tex]\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)[/tex] is given as:
[tex]\mathrm{y}-\mathrm{y}_{1}=\frac{\left(\mathrm{y}_{2}-\mathrm{y}_{1}\right)}{\left(\mathrm{x}_{2}-\mathrm{x}_{1}\right)}\left(\mathrm{x}-\mathrm{x}_{1}\right)[/tex]
[tex]\text { In our case } x_{1}=-5, y_{1}=4, x_{2}=5, y_{2}=1[/tex]
Substituting given value in (1) we get
[tex]\begin{array}{l}{y-4=\frac{(1-4)}{(5-(-5))}(x-(-5))} \\\\ {=>y-4=\frac{-3}{10}(x-(-5))} \\\\ {=>y-4=\frac{-3}{5}(x+5)}\end{array}[/tex]
Hence the point slope form of line is [tex]y-4=\frac{-3}{5}(x+5)[/tex]
