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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.
Here m is the slope and b is the y-intercept. This system specifies coordinates for all lines that are not vertical. However, it is more common and simpler algebraically to use coordinates (l, m) where the equation of the line is lx + my + 1 = 0. This system specifies coordinates for all lines except those that pass through the origin.
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
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).
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. x is the independent variable of the function y = f(x).
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. x is the independent variable of the function y = f(x).
a is frequently referred to as the slope of the line, and b as the intercept. If a > 0 then the gradient is positive and the graph slopes upwards. If a < 0 then the gradient is negative and the graph slopes downwards. For a function (, …,) of any finite number of variables, the general formula is
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 ...