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hendricks_beginning_algebra_1e_ch1_3

Section 3.3 The Slope of a Line 233 Since the slope is the ratio of the change in y to the change in x, it tells us how to move from the y-intercept to another point on the line. Recall the numerator of the slope corresponds to the change in y, or the vertical movement between the two points, and the denominator of the slope corresponds to the change in x, or the horizontal movement between the two points. ���������������������� Graphing a Line Given Its Slope and y-Intercept Step 1: Plot the y-intercept (0, b). Step 2: Use the slope to determine another point on the line. a. The numerator of the slope tells us how many units to go up (if positive) or down (if negative) from the y-intercept. b. The denominator tells us how many units to move to the right (if positive) or left (if negative). Step 3: Draw the graph of the line through these two points. ���������� y = mx + b → b tells us where to begin and m tells us how to move. �� ������������������������ ������������������ Graph the line using its slope and y-intercept. 3a. y = 3x + 2 3b. y=- 2 3 x + 2 Solutions 3a. In the equation, y = 3x + 2, the slope m = 3 and the y-intercept is (0, 2). Step 1: Plot the y-intercept (0, 2). Step 2: Since m = 3 = 3 1 , we move up 3 units as we move right 1 unit to get to another point. 6 2 –4 –2 2 x 4 4 –2 y (0, 2) Right 1 (1, 5) Up 3 2 –4 –2 2 x 6 4 –2 y (0, 2) Step 3: Connect the points to obtain the graph of y = 3x + 2. (1, 5) 4 2 –4 –2 2 x 6 4 –2 y (0, 2)


hendricks_beginning_algebra_1e_ch1_3
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