Example 3 What is the equation of the vertical line that goes through the point

# Example 3 what is the equation of the vertical line

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Example 3: What is the equation of the vertical line that goes through the point (5, 1) ?
MTH 111 College Algebra CHAPTER 2 NOTES Kelkenberg 6 S ECTION 2.5: S LOPE AND A VERAGE R ATE OF C HANGE Definition : The slope of a line is the ratio of the vertical change to the horizontal change (rise over run). If points ( 𝑥𝑥 1 , 𝑦𝑦 1 ) and ( 𝑥𝑥 2 , 𝑦𝑦 2 ) are any two distinct points on the line, then the slope of the line on which they lie is 𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑖𝑖 = 𝑚𝑚 = 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑦𝑦 2 −𝑦𝑦 1 𝑥𝑥 2 −𝑥𝑥 1 .
MTH 111 College Algebra CHAPTER 2 NOTES Kelkenberg 7 Example 1: Find the slope of the line below. a) b) Example 2: Find the slope of the line through (-2, 1) and (5, -4). Parallel & Perpendicular Lines Parallel Lines – The lines are parallel if and only if they have _______________________________. Perpendicular Lines – The lines are perpendicular if and only if their ____________ ___________________________________ of each other.
MTH 111 College Algebra CHAPTER 2 NOTES Kelkenberg 8 S ECTION 2.6: L INEAR F UNCTIONS The equation of a line with slope m and y -intercept b is always given by _____________________________________ Example 1: Find and graph the equation of the line. a) 𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑖𝑖 = 4 3 , 𝑦𝑦 − 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = (0, 3). b) 𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑖𝑖 = 2, 𝑦𝑦 − 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = (0, 4) Example 2: Find and graph the equation of the line. a) 𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑖𝑖 = 2 3 , ( 6, 4). b) 𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑖𝑖 = 0, (4, 5) c) 𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑖𝑖 = 𝑢𝑢𝑖𝑖𝑢𝑢𝑖𝑖𝑢𝑢𝑖𝑖𝑖𝑖𝑖𝑖𝑢𝑢 , ( 2, 3)
MTH 111 College Algebra CHAPTER 2 NOTES Kelkenberg 9 Example 3: Find the slope and y-intercept and then graph the line. a) 2 𝑥𝑥 + 𝑦𝑦 = 4 b) 𝑥𝑥 − 2 𝑦𝑦 = 2 Example 4: Graphically find the equation of the line that goes through both points. a) (0, 2) 𝑎𝑎𝑖𝑖𝑢𝑢 (4, 6) b) (4, 2) 𝑎𝑎𝑖𝑖𝑢𝑢 (2, 2)
MTH 111 College Algebra CHAPTER 2 NOTES Kelkenberg 10 Example 5: Graph and find the equation of the line that is a) parallel to 2 𝑥𝑥 + 4 𝑦𝑦 = 8 and passes through (2, 2) b) parallel to 𝑥𝑥 − 2 𝑦𝑦 = 4 and passes through ( 1, 1) Example 6: Graph and find the equation of the line that is a) perpendicular to 2 𝑥𝑥 + 4 𝑦𝑦 = 8 and passes through (2, 2) b) perpendicular to 𝑥𝑥 − 2 𝑦𝑦 = 4 and passes through ( 1, 1)
MTH 111 College Algebra CHAPTER 2 NOTES Kelkenberg 11 Point Slope Formula The equation of the line through ( 𝑥𝑥 1 , 𝑦𝑦 1 ) with slope m is given by 𝑦𝑦 − 𝑦𝑦 1 = 𝑚𝑚 ( 𝑥𝑥 − 𝑥𝑥 1 ) We use this form to find the equation of a line when we are given one point and the slope, or two points on the line.

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