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Answer:
Function that fits the points [tex](0,5),\,(2,-13)[/tex] is given by [tex]x+9y=45[/tex]
Step-by-step explanation:
Let [tex](x_1,y_1)=(0,5),\,(x_2,y_2)=(2,-13)[/tex]
Slope of a line joining points [tex](x_1,y_1),\,(x_2,y_2)[/tex] is given by [tex]m=\frac{x_2-x_1}{y_2-y_1}[/tex]
[tex]=\frac{2-0}{-13-5}[/tex]
[tex]=\frac{2}{-18}[/tex]
[tex]=\frac{-1}{9}[/tex]
Equation of a line joining points [tex](x_1,y_1),\,(x_2,y_2)[/tex] is given as follows:
[tex]y-y_1=m (x-x_1)[/tex]
[tex]y-5=\frac{-1}{9}(x-0)\\y-5=\frac{-1}{9}x\\9(y-5)=-x\\9y-45=-x\\x+9y=45[/tex]