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Y-intercept. Graph with the -axis as the horizontal axis and the -axis as the vertical axis. The -intercept of is indicated by the red dot at . In analytic geometry, using the common convention that the horizontal axis represents a variable and the vertical axis represents a variable , a -intercept or vertical intercept is a point where the ...
Comparison of Linear, Concave, and Convex Functions In original (left) and log10 (right) scales. In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form – appear as straight ...
The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding section. If b = 0, the line is a vertical line (that is a line parallel to ...
The x and y coordinates of the point of intersection of two non-vertical lines can easily be found using the following substitutions and rearrangements. Suppose that two lines have the equations y = ax + c and y = bx + d where a and b are the slopes (gradients) of the lines and where c and d are the y-intercepts of the lines.
Arrhenius plot. In chemical kinetics, an Arrhenius plot displays the logarithm of a reaction rate constant, ( , ordinate axis) plotted against reciprocal of the temperature ( , abscissa ). [1] Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions. For a single rate-limited thermally activated ...
In enzyme kinetics, a secondary plot uses the intercept or slope from several Lineweaver–Burk plots to find additional kinetic constants. [1] [2] For example, when a set of v by [S] curves from an enzyme with a ping–pong mechanism (varying substrate A, fixed substrate B) are plotted in a Lineweaver–Burk plot, a set of parallel lines will ...
An illustration of Newton's method. In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real -valued function. The most basic version starts with a real-valued ...
The design matrix is defined to be a matrix such that (the jth column of the ith row of ) represents the value of the jth variable associated with the ith object. A regression model may be represented via matrix multiplication as. where X is the design matrix, is a vector of the model's coefficients (one for each variable), is a vector of ...