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SteamKing said:Funny how the axes don't use evenly spaced divisions. I wonder why?
No, it's not semi-log. It is log-log. Both axes are logarithmically scaled.mri44 said:It is a semi Log graph.
Dickfore said:ok, your plot is semi-log, with the x-axis being a log scale and the y-axis being a linear scale, and the graph looks like a straight line. This means that your general equation is:
[tex]
y = a + b \, \log{x}
[/tex]
where the [itex]\log[/itex] is in whatever base you like (I would say decade), but the coefficient [itex]b[/itex] depends on your choice for a base. Then, you can use the method of least squares to get the points.
HallsofIvy said:Whatever the scale, that graph is a straight line so its equation is linear: y= ax+ b.
If it is in fact "log-log", and we call the vertical axis variable "V" and the horizontal axis variable "U", then the equation is log(V)= a(log(U))+ b. Take any two points on the graph and put their values into that equation. That gives two linear equations for a and b.
Taking the exponential of both sides, that equation becomes
[tex]e^{log(V)}= e^{alog(U)+ b}= e^{alog(U)}e^b= (e^b)(e^{log(U)})^a[/tex]
or
[tex]V= (e^b)U^a[/tex]
Finding the equation of a graph allows us to represent the relationship between variables in a mathematical form. This can help us make predictions, analyze patterns, and solve problems related to the data shown in the graph.
To find the equation of a graph, we need to determine the slope and y-intercept of the line represented in the graph. This can be done by selecting two points on the line and using the slope formula (y2-y1)/(x2-x1) to calculate the slope, and then substituting the coordinates of one of the points into the slope-intercept form of a line, y = mx + b, where m represents the slope and b represents the y-intercept.
Yes, the equation of any type of graph can be found as long as it represents a linear relationship between two variables. For nonlinear graphs, other methods such as curve fitting can be used to find an equation that best fits the data.
Finding the equation of a graph allows us to understand the relationship between the variables and make predictions based on the data. It also helps us analyze patterns and trends, and can be used to solve problems related to the data shown in the graph.
Yes, there are multiple methods to find the equation of a graph, such as using the slope-intercept form, point-slope form, or standard form. The method used may depend on the given information and personal preference.