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Conversely, every line is the set of all solutions of a linear equation. 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 ...
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 ...
A linear function is a polynomial function in which the variable x has degree at most one: [2] = +. Such a function is called linear because its graph, the set of all points (, ()) in the Cartesian plane, is a line. The coefficient a is called the slope of the function and of the line (see below).
Lines in a Cartesian plane or, more generally, in affine coordinates, are characterized by linear equations. More precisely, every line (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is, = {(,) + =}, where a, b and c are fixed real numbers (called coefficients) such that a and b are ...
In this case, the slope of the fitted line is equal to the correlation between y and x corrected by the ratio of standard deviations of these variables. The intercept of the fitted line is such that the line passes through the center of mass (x, y) of the data points.
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. At the point where the two lines intersect (if they do), both y coordinates will be the same, hence the following equality:
A linear equation in line coordinates has the form al + bm + c = 0, where a, b and c are constants. Suppose (l, m) is a line that satisfies this equation.If c is not 0 then lx + my + 1 = 0, where x = a/c and y = b/c, so every line satisfying the original equation passes through the point (x, y).
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.