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Ch. 2 Notes Page 7 P7 2.2: Linear Equations Part 1 “Friendship is born at that moment when one person says to another, ‘What! You too? I thought I was the only one.’” -C. S. Lewis “Failure is not falling down, but refusing to get back up.” – Chinese Proverb Linear Functions/Equations • A function whose graph is a line is a Linear Function • A linear function can be represented with a Linear Equation y=2x+4 •A solution is an (x,y) that makes the equation true. Graphing Linear Equations y = mx + b • y is called the dependent variable because the value of y depends on x • x is called the independent (or control) variable Example: Using a table, graph the equation: 2 y x3 3 x y 2 x3 3 y (x, y) Standard Form Standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers and A, B ≠ 0. You can graph linear equations in standard form by finding the x- and y- intercepts Example: Graph x + y = -2 More Practice The equation 3x + 2y = 120 models the number of passengers who can sit in a train car. X is the number of adults and y is the number of children. What are the x- and y- intercepts? What do they represent? What is the domain? Range? Slope y (rise) slope x(run) Example: What is the slope of the line through the points (-3, 4) and (8, -1)? Example: What is the slope of the line through the points (-2,-2) and (4,2)? Slope (cont.) y (rise) slope x(run) What does it mean if the slope is zero? Undefined? 2.2: Linear Equations Part 1 HW #4: 2-2 P67 #3, 6, 8, 11-13, 17-19 “Friendship is born at that moment when one person says to another, ‘What! You too? I thought I was the only one.’” -C. S. Lewis “Failure is not falling down, but refusing to get back up.” – Chinese Proverb Ch. 2 Notes Page 8 P8 2.2: Linear Equations Part 2 “Friendship is born at that moment when one person says to another, ‘What! You too? I thought I was the only one.’” -C. S. Lewis “Failure is not falling down, but refusing to get back up.” – Chinese Proverb Types of Equations Slope-Intercept Form Standard Form Point-Slope Form y=mx+b Ax+By=C y-y1=m(x-x1) Horizontal Lines & Vertical Lines y=Number x=Number Parallel and Perpendicular Lines Slopes and Reciprocals Slope-Intercept Form y = mx + b m=3 and (2,4) Standard Form Ax+By=C 4x+8y=24 Find the x- and y-intercepts Point-Slope Form The line through the point (x1, y1) with slope m has the equation y – y1 = m(x – x1) Example: Find the equation of a line with slope point (-6, 2). Write it in standard form. 1 through the 3 Point-Slope Form The line through the point (x1, y1) with slope m has the equation y – y1 = m(x – x1) Example: Find the equation of a line through the points (-2, 3) and (1, 6). Write it in standard form. Slope-Intercept Form y = mx + b What is the slope of the line 4x + 6y = 18? What is the slope of: a horizontal line? a vertical line? parallel lines? perpendicular lines? Example: Write an equation through the point (3, 5) and perpendicular to the line 7x – 21y = 42 3 equations for a line Slope-intercept: y = mx + b slope y-intercept Point-slope: y – y1 = m ( x – x1 ) (x,y) point on line Standard Form: A x + B y = C numbers 2.2: Linear Equations Part 2 HW #5: 2-2 P68 #20, 24, 26, 30, 32, 36, 43, 45, “Friendship is born at that moment 48, 51, 57 when one person says to another, ‘What! You too? I thought I was the only one.’” -C. S. Lewis “Failure is not falling down, but refusing to get back up.” – Chinese Proverb