The equation in point-slope form of the line passing through [tex](1,2)[/tex] and [tex](2,5)[/tex] is [tex]y=3x-1[/tex]
To find the slope of the line is
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{5-2}{2-1} \\m=\frac{3}{1} \\m=3[/tex]
The equation of the line is given by
[tex]y=mx+c.........(1)[/tex]
We have to use one point form to find the equation
The point [tex](1,2)[/tex] satisfies the equation
plug in the value of m, the equation becomes
[tex]2=3(1)+c\\2=3+c\\c=2-3\\c=-1[/tex]
Put the value of m,c in (1) equation
[tex]y=3x-1[/tex]
The equation of the line is [tex]y=3x-1[/tex].
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