Mon, 11/26 SWBAT… graph families of linear functions on a TI-83 graphing calculator Agenda 1. New seats / WU - (10 min) 2. Graphing calculator activity (40 min) Warm-Up: 1. Write your HW in your planner for the week 2. Review your test corrections and grade on the top right of your test in red. HW: Get Ready for Chapter 4 (back of agenda)

We have begun a new unit on linear functions: Students will be able to: 1. Write and interpret x-and y-intercepts (HW1 / HW2) 2. Graph lines using x-and y-intercepts (HW1 / HW2) 3. Calculate and interpret slope (HW3) 4. Write equations of lines (HW4) 5. Graph lines in slope-intercept form (HW5) 6. Write equations in slope-intercept form (HW6 / HW9) 7. Write equations in point-slope form (HW7 / HW9) 8. Write equations in standard from (HW8 / HW9) 9. Determine lines of best fit (HW10) 10. Parallel and perpendicular lines (HW11) Teachers mapping project after Winter break! Unit test after Winter break (1/24/13)! Final exam during the week of 1/28/13!

Today, you will be using the TI-83 graphing calculators to graph families of linear functions Your goal is to make conclusions on some characteristics of linear functions and to remember slope and y-intercept. Keep in mind the parent linear function, y = x

Conclusion A: Whatever the y-intercept is, that is where it crosses the y-axis.

SWBAT… find x- and y-intercepts algebraically and graphically. Agenda 1. Finish graphing calculator activity from yesterday AND 1. Correct your answers that are circled in blue. 2. Binder Check (10 min) 3. Work on back of agenda (20 min) 4. Graphing a line (10 min) 1. Graph 2x – y = -1 using a table of values 2. Circle and label the point where the line crosses the x-axis 3. Circle and label the point where the line crosses the y-axis Review PPT1: x-and y-intercepts Tues, 11/27

x y = 2x + 1

What does it mean to INTERCEPT a pass in football? The path of the defender crosses the path of the thrown football.

x- and y-intercepts The x-intercept is the point at which the graph crosses the x-axis (the y-coordinate is always 0 ) x-intercept = ( x, 0 ) The y-intercept is the point at which the graph crosses the y-axis (x-coordinate is always 0 ) y-intercept = ( 0, y ) Also called the Zero-Zero Method (2, 0) (0, -6) y

Directions: Find the x- and y-intercepts Ex1: 2x – y = -1 x-int. y = 0 2x – y = -1 2x – 0 = -1 2x = -1 x = -1/2 (-1/2, 0) y-int. x = 0 2x – y = -1 2(0) – y = -1 -y = -1 y = 1 (0, 1)

Now go back and look at your WU line Q: What was the x-intercept graphically? A: (-1/2, 0) Q: What was the x-intercept algebraically? A: (-1/2, 0) Q: What was the y-intercept graphically? A: (0, 1) Q: What was the y-intercept algebraically? A: (0, 1)

What are the x- and y-intercepts? xy x-int: (-2, 0) y-int: (0, 2)

Graphing linear equations To graph a linear equation you can use: 1.) Table of values (last week) 2.) Intercepts (right now!) 3.) Slope intercept form (y = mx + b) (next week)

2x – y = -1 Graph 2x – y = -1 using x- and y- intercepts To graph lines using x- and y-intercepts: Step 1: Find the x- and y-intercepts. x-int: (-1/2, 0) y-int: (0, 1) Step 2: Plot the two points. Step 3: Connect the points, extend the line, arrows at end, label the line. x 2x – y = -1

x-int. y = 0 3x – 5y = 9 3x – 5(0) = 9 3x = 9 x = 3; (3, 0) y-int. x = 0 3x – 5y = 9 3(0) – 5y = 9 -5y = 9 y = - ; (0, - ) Graph 3x – 5y = 9 using x- and y-intercepts

To graph lines using x- and y- intercepts: Step 1: Find the x- and y- intercepts. x-int: (3, 0) y-int: (0, -1.8) Step 2: Plot the two points. Step 3: Connect the points, extend the line, arrows at end, label the line. x 3x – 5y = 9

SWBAT… interpret x- and y-intercepts Agenda 1. Warm-Up (10 min) 2. Standard form, Ax + By = C (10 min) 3. x- and y-intercepts; special cases (15 min) 4. Interpreting x and y intercepts (10 min) Warm-Up: 1. Graph 2x + 5y = -10 using x- and y- intercepts. 2. Solve for y: Ax + By = C HW#2: Interpreting x-and y-intercepts Tues, 11/22

In the last three examples the equation of line was called Standard Form, Ax + By = C  2x – y = -1  3x – 5y = 9  2x + 5y = -10

Solve for y: Ax + By = C When an equation is given in the form Ax + By = C, the slope is:

x-int. Let y = 0 y = 3 0 = 3 0 = 3??? No! There is no x-intercept. None y-int. Let x = 0 y = 3 (y is already solve for) (0, 3) What type of lines have no x-intercept? Horizontal! Find the x- and y-intercepts of y = 3 ***Special case*** y = 3

x-int. Let y = 0 x = -4 (x is already solved for) (-4, 0) y-int. Let x = 0 x = -4 0 = -4??? No, there is no y-intercept. None What type of lines have no y-intercept? Vertical! Find the x- and y-intercepts of x = -4 ***Special case*** x = -4

What is the x-intercept of 3x – 4y = 24? 1. (-6, 0) 2. (8, 0) 3. (0, -4) 4. (8, -6)

What is the y-intercept of -x + 2y = 8? 1. (-1, 0) 2. (-8, 0) 3. (0, 2) 4. (0, 4)

What is the x-intercept of y = 1? (Hint: Draw this graph) 1. (1, 0) 2. (-1, 0) 3. (0, 1) 4. None

What is the y-intercept of y = 1? (Hint: Draw this graph) 1. (1, 0) 2. (-1, 0) 3. (0, 1) 4. None

What is the y-intercept of x = 3? (Hint: Draw this graph ) 1. (3, 0) 2. (-3, 0) 3. (0, 3) 4. None

HW#1 Answers 1. x-int = (3, 0) y-int = (0, 5) 2. x-int = (7, 0) y-int = (0, -2) 3. x-int = (0, 0) y-int = (0, 0)