Search results
Results From The WOW.Com Content Network
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
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.
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).
An example of a linear function is the function defined by () = (,) that maps the real line to a line in the Euclidean plane R 2 that passes through the origin. An example of a linear polynomial in the variables X , {\displaystyle X,} Y {\displaystyle Y} and Z {\displaystyle Z} is a X + b Y + c Z + d . {\displaystyle aX+bY+cZ+d.}
If a = 0 and b ≠ 0, the line is horizontal and has equation y = -c/b. The distance from (x 0, y 0) to this line is measured along a vertical line segment of length |y 0 - (-c/b)| = |by 0 + c| / |b| in accordance with the formula. Similarly, for vertical lines (b = 0) the distance between the same point and the line is |ax 0 + c| / |a|, as ...
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.
Because the lines are parallel, the perpendicular distance between them is a constant, so it does not matter which point is chosen to measure the distance.
In the equation y = Cx, C is the scale factor for x. C is also the coefficient of x, and may be called the constant of proportionality of y to x. For example, doubling distances corresponds to a scale factor of two for distance, while cutting a cake in half results in pieces with a scale factor for volume of one half.