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The equation of the line passing through the two points [tex](1,1)[/tex] and [tex](3,5)[/tex] is [tex]\frac{3}{1}[/tex] i.e. [tex]y=2x-1[/tex]
For finding the equation of lien if two points are given then we will use the two-point form i.e.
[tex]y-y_{1}=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } (x-x_{1})[/tex]
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{5-1}{3-1} \\m=\frac{4}{2} \\m=\frac{2}{1}\\m=2[/tex]
The slope of the line is [tex]2[/tex]
The point [tex](x_{1} ,y_{1} )=(1,1)[/tex]
Plug in these values
[tex]y-1=2(x-1)\\y-1=2x-2\\y=2x-2+1\\y=2x-1[/tex]
The equation of the line is [tex]y=2x-1[/tex]
Learn more about equations from
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