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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 graph of a function or relation intersects the -axis of ...
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.
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).
Given distinct points A and B, they determine a unique ray with initial point A. As two points define a unique line, this ray consists of all the points between A and B (including A and B) and all the points C on the line through A and B such that B is between A and C. [12]
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 y = a x k {\displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the exponent corresponding to ...
Lines in a Cartesian plane, or more generally, in affine coordinates, can be described algebraically by linear equations. In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form: = + where: m is the slope or gradient of the line. b is the y-intercept of the line.
Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation. In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
The formulas given in the previous section allow one to calculate the point estimates of α and β — that is, the coefficients of the regression line for the given set of data. However, those formulas do not tell us how precise the estimates are, i.e., how much the estimators α ^ {\displaystyle {\widehat {\alpha }}} and β ^ {\displaystyle ...