Section 3.3 The Slope of a Line 227 This means that for each 2 units of change in the y-coordinates, there is a corresponding change of 1 unit in the x-coordinates. Note: The slope of the line is the same for every pair of points on the line. If the slope is not the same, then the graph is not a line. Definition: The slope of a line is the ratio of the change in y to the change in x between two points on a line. The slope is denoted by the letter m. It is often called “vertical change over horizontal change” or “rise over run.” m = Change in y Change in x = vertical change horizontal change = rise run Using a table of values to find the slope of a line can become quite cumbersome. We can also find the slope of a line by using the slope formula. Property: The Slope Formula If (x1, y1) and (x2, y2) are two points that lie on a line with x1 ≠ x2, then the slope is m = change in y change in x = y2 - y1 x2 - x1 = y1 - y2 x1 - x2 If x1 = x2, then the line through the points is vertical and the slope is undefined. x2 – x1 x2, y2 Procedure: Using the Slope Formula to Find the Slope between Two Points Step 1: Label one point as (x1, y1) and the otherpoint as (x2, y2). Step 2: Substitute the values into the formula m = y2 - y1 x2 - x1 Step 3: Simplify the numerator and denominator and reduce the fraction, if necessary. Objective 1 Examples Use the slope formula to determine the slope between each pair of points. 1a. (-1, -2) and (4, 5) 1b. (5, -3) and (-4, 2) 1c. (2, -3) and (2, 5) 1d. (0, -2) and (4, -2) 1e. x y y2 – y1 x1, y1 6 2 –2 2 x 4 4 –2 y
hendricks_beginning_intermediate_algebra_1e_ch1_3
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