TAILIEUCHUNG - Theatex as higher education assessment_6

Tham khảo tài liệu 'theatex as higher education assessment_6', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | THEA MATH REVIEW The slope of a line can be found if you know the coordinates of any two points that lie on the line. It does not matter which two points you use. It is found by writing the change in the y-coordinates of any two points on the line over the change in the corresponding x-coordinates. This is also known as the rise over the run. The formula for the slope of a line or line segment containing points x1 y1 and x2 y2 m - . Example Determine the slope of the line joining points A -3 5 and B 1 -4 . m Let x1 y1 represent point A and let x2 y2 represent point B. This means that x1 -3 y1 5 x2 1 and y2 -4. Substituting these values into the formula gives us y2 1 x2- Xi m -4-5 1 - -3 m AL 4 Example Determine the slope of the line graphed below. Two points that can be easily determined on the graph are 3 1 and 0 -1 . Let 3 1 x1 y1 and let 0 -1 x2 y2 . This means that x1 3 y1 1 x2 0 and y2 -1. Substituting these values into the formula gives us 146 THEA MATH REVIEW -1-1 m m Í3 2 Note If you know the slope and at least one point on a line you can find the coordinate point of other points on the line. Simply move the required units determined by the slope. For example from 8 9 given the slope ý move up seven units and to the right five units. Another point on the line thus is 13 16 . Determining the Equation of a Line The equation of a line is given by y mx b where y and x are variables such that every coordinate pair x y is on the line m is the slope of the line b is the -intercept the y-value at which the line intersects or intercepts the y-axis In order to determine the equation of a line from a graph determine the slope and y-intercept and substitute it in the appropriate place in the general form of the equation. Example Determine the equation of the line in the graph below. 147 THEA MATH REVIEW In order to determine the slope of the line choose two points that can be easily determined on the graph. Two easy points are -1 4 and 1 -4 . Let -1 4 Xpy1 and let 1 -4

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