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.
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.
- 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.