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 Ch. 2 Notes Page 7 P7 2.2: Linear Equations Part 1 “Failure is not falling down, but refusing to get back up.” – Chinese Proverb

2. 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.

3. 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 : xy(x, y)

4. 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

5. 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?

6. Slope 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)?

7. Slope (cont.) What does it mean if the slope is zero? Undefined?

8. “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 2.2: Linear Equations Part 1 HW #4: 2-2 P67 #3, 6, 8, 11-13, 17-19

9. “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 Ch. 2 Notes Page 8 P8 2.2: Linear Equations Part 2 “Failure is not falling down, but refusing to get back up.” – Chinese Proverb

10. Types of Equations Slope-Intercept Formy=mx+b Standard FormAx+By=C Point-Slope Formy-y 1 =m(x-x 1 ) Horizontal Lines & Vertical Lines y=Numberx=Number Parallel and Perpendicular Lines Slopes and Reciprocals

11. Slope-Intercept Form y = mx + b m=3 and (2,4)

12. Standard Form Ax+By=C 4x+8y=24Find the x- and y-intercepts

13. Point-Slope Form The line through the point (x 1, y 1 ) with slope m has the equation y – y 1 = m(x – x 1 ) Example: Find the equation of a line with slope through the point (-6, 2). Write it in standard form.

14. Point-Slope Form The line through the point (x 1, y 1 ) with slope m has the equation y – y 1 = m(x – x 1 ) Example: Find the equation of a line through the points (-2, 3) and (1, 6). Write it in standard form.

15. 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

16. 3 equations for a line Slope-intercept: y = mx + b slopey-intercept Point-slope: y – y 1 = m ( x – x 1 ) (x,y) point on line Standard Form: A x + B y = C numbers

17. “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 2.2: Linear Equations Part 2 HW #5: 2-2 P68 #20, 24, 26, 30, 32, 36, 43, 45, 48, 51, 57