Search results
Results from the WOW.Com Content Network
The Keynesian cross diagram includes an identity line to show states in which aggregate demand equals output. In a 2-dimensional Cartesian coordinate system, with x representing the abscissa and y the ordinate, the identity line [1] [2] or line of equality [3] is the y = x line. The line, sometimes called the 1:1 line, has a slope of 1. [4]
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).
Vertical line of equation x = a Horizontal line of equation y = b. Each solution (x, y) of a linear equation + + = may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that a and b are not both zero. Conversely, every line is the set of all ...
Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
For example, the upper right branch of the curve y = 1/x can be defined parametrically as x = t, y = 1/t (where t > 0). First, x → ∞ as t → ∞ and the distance from the curve to the x-axis is 1/t which approaches 0 as t → ∞. Therefore, the x-axis is an asymptote of the curve.
Also, let Q = (x 1, y 1) be any point on this line and n the vector (a, b) starting at point Q. The vector n is perpendicular to the line, and the distance d from point P to the line is equal to the length of the orthogonal projection of Q P → {\displaystyle {\overrightarrow {QP}}} on n .
Horner's method can be used to convert between different positional numeral systems – in which case x is the base of the number system, and the a i coefficients are the digits of the base-x representation of a given number – and can also be used if x is a matrix, in which case the gain in computational efficiency is even greater.