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A line passes through points (3,20) and (8,25). Write a linear function rule in terms of x and y for this line.

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To find:-

  • The equation of line passing through the points (3,20) and (8,25) .

Answer:-

To find out the equation of the line , we need to find out the slope first. It can be calculated as ,


\implies m =(\Delta y)/(\Delta x )=(y_2-y_1)/(x_2-x_1) \\

And here ,


  • y_1 = 20

  • y_2 = 25

  • x_1 = 3

  • x_2 = 8

On substituting the respective values, we have;


\implies m =(25-20)/(8-3) \\


\implies m=(5)/(5)\\


\implies m=\boxed{1} \\

Hence the slope of the line is 1 . Now we may use point slope form of the line to find out the equation of the line. Point slope form of the line is,


\implies y - y_1 = m(x-x_1) \\

Take any of the given two points. Here i am taking (3,20) . So here we have;


  • m = 1

  • y_1 = 20

  • x_1 = 3

On substituting the respective values, we have;


\implies y - 20 = 1(x - 3) \\


\implies y -20 = x - 3 \\


\implies x - 3 - y +20 = 0 \\


\implies \underline{\underline{\green{ x - y +17=0}}}\\

Hence the equation of the line in standard form is x - y + 17 = 0 .

and we are done!

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