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The -intercept of () is indicated by the red dot at (=, =). In analytic geometry , using the common convention that the horizontal axis represents a variable x {\displaystyle x} and the vertical axis represents a variable y {\displaystyle y} , a y {\displaystyle y} -intercept or vertical intercept is a point where the graph of a function or ...
When plotted in the manner described above, the value of the y-intercept (at = / =) will correspond to (), and the slope of the line will be equal to /. The values of y-intercept and slope can be determined from the experimental points using simple linear regression with a spreadsheet .
The y-intercept point (,) = (,) corresponds to buying only 4 kg of sausage; while the x-intercept point (,) = (,) corresponds to buying only 2 kg of salami. Note that the graph includes points with negative values of x or y , which have no meaning in terms of the original variables (unless we imagine selling meat to the butcher).
Linear interpolation on a data set (red points) consists of pieces of linear interpolants (blue lines). Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points.
A non-vertical line can be defined by its slope m, and its y-intercept y 0 (the y coordinate of its intersection with the y-axis). In this case, its linear equation can be written = +. If, moreover, the line is not horizontal, it can be defined by its slope and its x-intercept x 0. In this case, its equation can be written
x, y, and z are all functions of the independent variable t which ranges over the real numbers. ( x 0 , y 0 , z 0 ) is any point on the line. a , b , and c are related to the slope of the line, such that the direction vector ( a , b , c ) is parallel to the line.
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
The above equations are efficient to use if the mean of the x and y variables (¯ ¯) are known.If the means are not known at the time of calculation, it may be more efficient to use the expanded version of the ^ ^ equations.