Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions First Name: ________________________ Last Name: ________________________ Block: ______ Ch. 6 – Linear Functions Notes 6.1 – SLOPE OF A LINE 2 Ch. 6.1 HW: p. 339 #4 – 13, 17, 23, 25, 28 5 6. 2 – SLOPES OF PARALLEL AND PERPENDICULAR LINES 6 Ch. 6.2 HW: p. 349 #3 – 6 odd letters, 7 – 20 8 6.3 – INVESTIGATING GRAPHS OF LINEAR FUNCTIONS 9 6.4 – SLOPE‐INTERCEPT FORM OF THE EQUATION FOR A LINEAR FUNCTION 13 Ch. 6.4 HW: p. 362 # 4 – 9, 12, 13 – 16 15 6.5 – SLOPE‐POINT FORM OF THE EQUATION FOR A LINEAR FUNCTION 16 Ch. 6.5 HW: p. 372 #4 – 14, 19 – 25 19 6.6 – GENERAL FORM OF THE EQUATION FOR A LINEAR RELATION 20 Ch. 6.6 HW: p. 384 #4 – 9, 12 – 14, 18, 22 – 24 22 CH. 6 REVIEW – LINEAR FUNCTIONS 23 Created by Ms. Lee 1 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions 6.1 – Slope of a Line rise Definition: Slope = run In order to move from A to E, you need to move ____ units _____ and ____ units _______. Rise = ________ ; Run = ________ rise The measure of of a line is called the slope. run Slope = In order to move from E to A, you need to move ____ units _____ and ____ units _______. Rise = ________ ; Run = ________ rise The measure of of a line is called the slope. run Slope = Examples: Determining the Slope of a Line Segment 1) Find two exact points on the graph 2) Determine the rise and run 3) Determine the slope. Created by Ms. Lee 2 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions Examples: Noticing the Patterns Examples: Drawing a Line Segment with a Given Slope and a Point. Draw a line segment with each given slope. 2 4 Slope = through (0, -2) through (-4, 3) 3 5 Created by Ms. Lee 3 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions Examples: Determining Slope Given Two Points on a Line. Rise y y Slope = 2 2 Run x2 x1 Determine the slope of the line that passes Determine the slope of the line that passes through C(-3, 5) and D(2, 1) using the above through C(-3, 5) and D(2, 1) by sketching the formula. line segment Determine the slope of the line that passes Determine the slope of the line that passes through A(-4, 3) and B(2, -5) using the above through A(-4, 3) and B(2, -5) by sketching the formula. line segment Created by Ms. Lee 4 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions Examples: Interpreting the Slope of a Line Yvonne recorded the distance she travelled at certain times since she began her cycling trip along the Trans Canada Trail in Manitoba, from North Winnipeg to Grand Beach. She plotted these data on a grid. a) What is the slope of the line through these points? b) What does the slope represent? 3 c) How can the answer to part b be used to determine how far Yvonne travelled in 1 hours? 4 d) How can the answer to part b be used to determine the time it took Yvonne to travel 55km? Multiple Choice Question: 1) A line with an undefined slope passes through the points (-2 , 1) and (p , q). Which of the following points could be (p , q)? A. (1, 0) B. (0 , 1) C. (0 , -2) D. (-2 , 0) Ch. 6.1 HW: p. 339 #4 – 13, 17, 23, 25, 28 Created by Ms. Lee 5 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions 6. 2 – Slopes of Parallel and Perpendicular Lines Definition: Parallel lines: Parallel lines are lines that never intersect (meet). Line A and Line B are parallel lines. Determine the slope of each line segment. Slope of Line A = Slope of Line B = Line A and Line B are parallel lines. Determine the slope of each line segment. Slope of Line A = Slope of Line B = If two lines are parallel, their slopes are _____________________. Examples: Identifying Parallel Lines Line AB passes through A(-3, -2) and B(-1, 6). Line CD passes through C(-1, -3) and D(1, 7). Line EF passes through E(2, -5) and F(4, 3). Sketch the lines. Are they parallel? Justify the answer. Created by Ms. Lee 6 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions Definition: Perpendicular lines: Perpendicular lines are lines that intersect at a 90 angle. Line A and Line B are perpendicular lines. Determine the slope of each line segment. Slope of Line A = Slope of Line B = Line A and Line B are perpendicular lines. Determine the slope of each line segment. Slope of Line A = Slope of Line B = If two lines are perpendicular, their slopes are _____________________. Examples: Identifying a Line Perpendicular to a Given Line. a) Determine the slope of a line that is perpendicular to the line through E(2,3) and F(-4, -1). b) Determine the coordinates of G so that line EG is perpendicular to line EF. Created by Ms. Lee 7 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions Definitions: x- intercept: x-value where the line intercepts the x-axis. y-intercept: y-value where the line intercepts the y-axis. Examples: 1) AB has an x-intercept of 3 and a y-intercept of -2. CD has an x-intercept of 2 and a y-intercept of 3. How are the lines related? Justify your answer. 2) The coordinates of the vertices of ABC are A(-1, 3), B(1, -2) and C(4, 5). Is it a right triangle? Justify your answer. Ch. 6.2 HW: p. 349 #3 – 6 odd letters, 7 – 20 Created by Ms. Lee 8 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions 6.3 – Investigating Graphs of Linear Functions Using a table of values, graph the linear functions. Any pattern you notice? y = 2x x y Slope = y-intercept = y = 4x + 1 x y Slope = y-intercept = y = x – 2 x y Slope = y-intercept = y = 3x – 4 x y Slope = y-intercept = Created by Ms. Lee 9 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions y = -3x x y Slope = y-intercept = y = -x + 2 x y Slope = y-intercept = y = -4x – 3 x y Slope = y-intercept = y = -2x – 5 x y Slope = y-intercept = In general, given a linear function in the Slope-Intercept Form: y = mx + b, m is the _____________ and b is the ___________________ Created by Ms. Lee 10 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions Questions: 1) What is the slope and y-intercept of each linear function? Linear functions Slope y-intercept a) y = 3x 4 1 b) y = x 5 2 3 c) y = x 2 d) y = 2x 3 2 e) y = x 1 5 3 f) y = x 5 g) y = x 4 h) y = 3x 5 i) y = 4 j) y = -3 2) Which of the function(s) in Question 1 is parallel to y = 3x 7 ? 1 3) Which of the function(s) in Question 1 is parallel to y = x 1? 2 4) Which of the function(s) in Question 1 is perpendicular to y = x 1? 5 5) Which of the function(s) in Question 1 is perpendicular to y = x 2 ? 2 Created by Ms. Lee 11 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions Graph each linear function without using table of values. 1) y 3x 1 2) y 3x 1 1 1 3) y x 3 4) y x 3 2 2 4 2 5) y x 1 6) y x 3 3 Created by Ms. Lee 12 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions 6.4 – Slope-Intercept Form of the Equation for a Linear Function Recap: Given a linear function in the Slope-Intercept Form, y = mx + b, m = slope b = y-intercept Questions: 6) What is the slope and y-intercept of each linear function? k) y = 3x 4 2 l) y = x 5 7 3 m) f(x) = x 2 4 Examples: Writing an Equation of a Linear Function Given Its Slope and y-intercept 1) The graph of a linear function has slope 3 and y-intercept 5. Write an equation for this function. 1 2) The graph of a linear function has slope and y-intercept 3 . Write an equation for this 2 function. Examples: Graphing a Linear Function Given its Equation in Slope-Intercept Form Graph each linear function: 1 2 1) y = x + 5 2) y = x 4 2 3 Created by Ms. Lee 13 of 26 Reference: Foundations and Pre-Calculus Mathematics 10, Pearson Foundations of Mathematics & Pre-Calculus 10 Chapter 6 – Linear Functions 3) y = 4x 1 4) y = 3x 2 4 1 5) y = x 6 6) y = x 2 5 3 Examples: Writing the equation of a Linear Function Given Its Graph Write an equation to describe this function.