# Given sets of experimental values of x and y, detemine the variables whose values should be plotted in order to obtain a straight line graph.It is expected that the variables x and y are related by...

Given sets of experimental values of x and y, detemine the variables whose values should be plotted in order to obtain a straight line graph.

It is expected that the variables x and y are related by the equation lg(ax+b) where a and b are unknown constants. Given sets of experimental values of x and y, detemine the variables whose values should be plotted in order to obtain a straight line graph, and explain how the graph may be used to determine the values of a and b.

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Now our equation is y = lg (ax+b)

In reality this graph is not a linear line. It has a curve shape. I have shown the graph of y = log (2x+3) for example.

But as for the experimental results and easy handling we can consider this as a linear function.

Using experimental results once you draw the graph you will get the equation as;

`y = lg(ax+b)`

We need to find a and b.

first consider the point where x = 0 and y=y1

`y0 = lg(a*0+b)`

`y0 = lgb`

`b = 10^(y0)`

Now let us consider any known point x=x1 and y=y1

`y1 ` = `lg(a*x1+b)`

`10^(y1)` = `a*x1+10^(y0)`

a = `[10^(y1)-10^(y0)]/(x1)`

Now we can find a using the above equation.

Note

- If the graph does not intercept x=0 line we can extrapolate the line to get that value.

- When finding a we can do it easily if we consider the point y=0 if possible.