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The simplest is the slope-intercept form: = +, from which one can immediately see the slope a and the initial value () =, which is the y-intercept of the graph = (). Given a slope a and one known value () =, we write the point-slope form:
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.
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).
the slope field is an array of slope marks in the phase space (in any number of dimensions depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (,,, …,) and is parallel to the vector
The fit line is then the line y = mx + b with coefficients m and b in slope–intercept form. [12] As Sen observed, this choice of slope makes the Kendall tau rank correlation coefficient become approximately zero, when it is used to compare the values x i with their associated residuals y i − mx i − b. Intuitively, this suggests that how ...
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