Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept 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 slope-intercept form. 1. Step1: Find the slope-intercept form of a linear line 2. Step2: Plot the first point, the y-intercept. 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 Cheon-Sig Lee Page 1
Excercises (Solution 1) The given equation y = 2x + 5 is in the form y = mx + b Step 2: Find the slope and y-intercept. The slope, m, is the coefficient of x. Thus, m = 2 The y-intercept, b, is constant. So, b=5 (Solution 2) y = x is in the form y = mx + b Step 2: Find the slope and y-intercept. 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 y-intercept 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 y-intercept m is the coefficient of x. So, m = 6 b, is constant. So, b= 5 Cheon-Sig Lee Page 2
(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 y-intercept 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 y-intercept 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 y-intercept. y-intercept 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 y-intercept, and then move 2 units up. Thus the second point is (1, 7) Cheon-Sig Lee Page
(Solution 8) y = x + 2 is in the form y = mx + b 8 Step 2: Plot the y-intercept y-intercept is (0, 2) Step : Plot the second point using the slope The slope is. Move 8 units to right from 8 the y-intercept, 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 y-intercept y-intercept is (0, 0) Step : Plot the second point using the slope 8 The slope is. Move units to right from the y-intercept, and then move 8 units down. Thus, the second point is (, 8) Cheon-Sig Lee Page 4
(Solution 10) a. 9x + y= 0 9x 9x y = 9x b. y = 9x y = 9x + 0 The slope is 9 and y-intercept is 0 c. Graph the line Step 1: Plot the y-intercept, (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 y-intercept. The y-intercept 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 Cheon-Sig Lee Page 5
(Solution 12) a. 5x + 4y = 20 5x 5x 4y= 5x + 20 4y 4 = 5x 4 + 20 4 y= 5 4 x + 5 b. Graph the line m = 5 4 ; b = 5 Step 1: Plot the y-intercept: (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) Cheon-Sig Lee Page 6
(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) Cheon-Sig Lee Page 7
(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) Cheon-Sig Lee Page 8