Section 3.4 The Slope Intercept Form: y = mx + b


 Robert Goodman
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1 SlopeIntercept Form: y = mx + b, where m is the slope and b is the yintercept Reminding! m = y x = y 2 y 1 x 2 x 1 Slope of a horizontal line is 0 Slope of a vertical line is Undefined Graph a linear line with the slopeintercept form. 1. Step1: Find the slopeintercept form of a linear line 2. Step2: Plot the first point, the yintercept. Step: Plot the second point using the given slope m = y x x is the changes in x; y is the changes in y. Move to right by x units. Move up y units if y is positive and Move down y units if y is negative. Parallel Lines: Lines that never intersect (cross each other) and these lines have same slope Two lines (neither vertical) are parallel if and only if they have the same slope All vertical lines are parallel m 1 = m 2 Perpendicular lines: Lines that intersect at 90 (right) angles and whose slopes are negative reciprocal of each other Two lines (neither vertical) are perpendicular if and only if their slopes are negative reciprocal of each other Vertical lines are perpendicular to horizontal lines 1 m 1 m 2 = 1 or m = 2 m 1 CheonSig Lee Page 1
2 Excercises (Solution 1) The given equation y = 2x + 5 is in the form y = mx + b Step 2: Find the slope and yintercept. The slope, m, is the coefficient of x. Thus, m = 2 The yintercept, b, is constant. So, b=5 (Solution 2) y = x is in the form y = mx + b Step 2: Find the slope and yintercept. m is the coefficient of x. So, m = 2 b, is constant. So, b= 5 (Solution ) y = 12 is in the form y = mx + b That is, y = 0x + 12 Step 2: Find the slope and yintercept m is the coefficient of x. So, m = 0 b, is constant. So, b= 12 (Solution 4) 6x + y = 5 is not in y = mx + b 6x + y = 5 +6x +6x y = 6x + 5 Now, y = 6x + 5 is not in y = mx + b Step 2: Find the slope and yintercept m is the coefficient of x. So, m = 6 b, is constant. So, b= 5 CheonSig Lee Page 2
3 (Solution 5) 9x + y= 0 9x 9x y = 9x Now, y = 9x is in y = mx + b That is, y = 9x + 0 Step 2: Find the slope and yintercept m is the coefficient of x. So, m = 9 b, is constant. So, b= 0 (Solution 6) y = x y = x y = 1 x 1 Now, y = x is in y = mx + b 1 That is, y = x+ 0 Step 2: Find the slope and yintercept m is the coefficient of x. So, m = 1 b, is constant. So, b= 0 (Solution 7) y = 2x + 5 is in the form y = mx + b Step 2: Plot the yintercept. yintercept is (0, 5) Step : Plot the second point using the slope The slope is 2 which means 2 1. Move 1 unit to the right from yintercept, and then move 2 units up. Thus the second point is (1, 7) CheonSig Lee Page
4 (Solution 8) y = x + 2 is in the form y = mx + b 8 Step 2: Plot the yintercept yintercept is (0, 2) Step : Plot the second point using the slope The slope is. Move 8 units to right from 8 the yintercept, and then move units down. Thus, the second point is (8, 1) (Solution 9) y = 8 x is in the form y = mx + b Step 2: Plot the yintercept yintercept is (0, 0) Step : Plot the second point using the slope 8 The slope is. Move units to right from the yintercept, and then move 8 units down. Thus, the second point is (, 8) CheonSig Lee Page 4
5 (Solution 10) a. 9x + y= 0 9x 9x y = 9x b. y = 9x y = 9x + 0 The slope is 9 and yintercept is 0 c. Graph the line Step 1: Plot the yintercept, (0, 0) using the slope. The second point is (1, 9) The graph is shown below (Solution 11) a. 6y= 5x 6y 6 = 5x 6 y= 5x 6 b. Graph the line m = 5 6 ; b = 0 Step 1: Plot the yintercept. The yintercept is (0, 0) Move 6 units to the right from the y intercept and then move 5 units up. So, the second point is (6, 5) The graph is shown below CheonSig Lee Page 5
6 (Solution 12) a. 5x + 4y = 20 5x 5x 4y= 5x y 4 = 5x y= 5 4 x + 5 b. Graph the line m = 5 4 ; b = 5 Step 1: Plot the yintercept: (0, 5) Move 4 units to the right from the y intercept, and then move 5 units up. Thus, the second point is (5, 0) (Solution 1) Graph y = x + 2 m = 1 = 1 1 ; b = 2 Step 1: Plot y intercept: (0, 2) intercept, and then move 1 unit down. The second point is (1, 1) Graph y = x 5 m = 1 = 1 ; b = 5 1 Step 1: Plot y intercept: (0, 5) intercept, and then move 1 unit down. The second point is (1, 6) CheonSig Lee Page 6
7 (Solution 14) Graph y = x + 2 m = = 1 ; b = 2 Step 1: Plot y intercept: (0, 2) intercept, and then move unit down. The second point is (1, 5) Graph y = x + 2 m = = 1 ; b = 2 Step 1: Plot y intercept: (0, 2) intercept, and then move unit up. The second point is (1, 5) CheonSig Lee Page 7
8 (Solution 15) Graph y = x + 4 m = 1 = 1 1 ; b = 4 Step 1: Plot y intercept: (0, 4) intercept, and then move 1 unit down. The second point is (1, ) Graph y = x 5 m = 1 = 1 1 ; b = 5 Step 1: Plot y intercept: (0, 5) intercept, and then move unit up. The second point is (1, 4) CheonSig Lee Page 8
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