Lesson 3.4 Graphing Horizontal and Vertical Lines Objective- To graph horizontal and vertical lines. Graph x + y = 5 x y -2 7 y -1 6 5 Line is oblique 1 4 2 3 3 2 4 1 x 5 6 -1 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

Graph. y = 3 Line is Horizontal x y y -2 3 -1 3 3 1 3 2 3 x 3 3 4 3 3 1 3 2 3 x 3 3 4 3 Any line in the form y = k will be horizontal. 5 3 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Graph. x = -2 Line is Vertical x y y -2 -2 -2 -1 -2 -2 1 -2 2 x -2 3 -2 1 -2 2 x -2 3 -2 4 Any line in the form x = k will be vertical. -2 5 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Types of Lines Ax + By = C y = k x = k 3x - 2y = 5 y = -7 Oblique Horizontal Vertical Equation form Ax + By = C y = k x = k Example 3x - 2y = 5 y = -7 Universal constants A = 3 k = -7 B = -2 C = 5 A, B and C are integers (no fractions or decimals). k represents a rational number. Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Review x = k y = k Horizontal Line Vertical Line Perpendicular to y-axis. Perpendicular to x-axis. Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

A) Graph x = -4 on a number line. -5 -4 -3 -2 -1 0 1 2 3 B) Graph x = -4 on a coordinate plane. y x Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

= where the line crosses the x-axis y-intercept Finding Intercepts x-intercept = where the line crosses the x-axis y-intercept = where the line crosses the y-axis Horizontal Vertical y = 2 x-int.= none x = -1 x-int.= -1 y-int.= 2 y-int.= none y y x x Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

= where the line crosses the x-axis y-intercept Finding Intercepts x-intercept = where the line crosses the x-axis y-intercept = where the line crosses the y-axis Oblique x-intercept y-intercept y = 2x + 3 (set y = 0) (set x = 0) y = 2x + 3 y = 2x + 3 x y y -3 -2 -1 1 2 0 = 2x + 3 y = 2(0) + 3 -3 -3 -3 -1 y = 3 -3 = 2x 1 x 2 2 3 5 7 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Find the x-intercept and y-intercept. x = 5 or (5,0) none 2) none 3) x = -1 (-1,0) none Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Find the x-intercept and y-intercept. 4) 4x + 2y = 6 (Set y = 0) (Set x = 0) 4x + 2y = 6 4x + 2y = 6 4x + 2(0) = 6 4(0) + 2y = 6 4x = 6 2y = 6 4 4 2 2 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Find the x-intercept and y-intercept. 5) 3x - y = -5 (Set y = 0) (Set x = 0) 3x - y = -5 3x - y = -5 3x - (0) = -5 3(0) - y = -5 3x = -5 -y = -5 3 3 -1(-y = -5) Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series