HW: Get Ready for Chapter 4 (back of agenda) Mon, 11/26 SWBAT… graph families of linear functions on a TI-83 graphing calculator Agenda WU - (10 min) Graphing calculator activity (35 min) Warm-Up: Write your HW in your planner for the week. Review your test corrections and your updated grade on the top right of your test in red. HW: Get Ready for Chapter 4 (back of agenda) 1

We have begun a new unit on graphs and linear functions: Students will be able to: Write and interpret x-and y-intercepts (HW1 / HW2) Graph lines using x-and y-intercepts (HW1 / HW2) Calculate and interpret slope (HW3) Graph lines in slope-intercept form (HW4) Write equations in slope-intercept form (HW4 / HW6) Write equations in point-slope form (HW5) Write equations in standard from (HW5) Determine lines of best fit (HW7) Write equations that are parallel or perpendicular (HW8) Unit test after Winter break on 1/17/13! 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

SWBAT… find x- and y-intercepts graphically and algebraically Wed, 11/28 SWBAT… find x- and y-intercepts graphically and algebraically Agenda Warm-Up (10 min) Notes on x- and y intercepts (15 min) OYO problems (10 min) Warm-Up: 1. Graph y – 1 = 2x 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 HW#1: x- and y-intercepts Solve for y (add 1 to both sides) 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 of a line is the point at which the line crosses the x-axis. ( i.e. where the y value equals 0 ) x-intercept = ( x, 0 ) The y-intercept of a line is the point at which the line crosses the y-axis. ( i.e. where the x value equals 0 ) y-intercept = ( 0, y )

Directions: Find the x- and y-intercepts Ex1: y = 2x + 1 x-int. y = 0 y = 2x + 1 0 = 2x + 1 -2x = 1 x = -1/2 (-1/2, 0) y-int. x = 0 y = 2x + 1 y = 2(0) + 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? Q: What was the y-intercept graphically? A: (0, 1) Q: What was the y-intercept algebraically?

What are the x- and y-intercepts? (2, 0) x The x-intercept is where the graph crosses the x-axis. The y-coordinate is always 0. The y-intercept is where the graph crosses the y-axis. The x-coordinate is always 0. (0, -6)

Directions: Find the x- and y-intercepts Ex2: -3x + 5y = 9 x-int. y = 0 -3x + 5y = 9 -3x + 5(0) = 9 -3x = 9 x = -3; (-3, 0) y-int. x = 0 -3(0) + 5y = 9 5y = 9 y = ; (0, )

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 project)

Graph y = 2x + 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.

Find the x- and y-intercepts Ex3: y = 3 ***Special case*** x-int. Let y = 0 y = 3 0 = 3 0 = 3??? No! There is no x-intercept. None What type of lines have no x-intercept? Horizontal! y-int. Let x = 0 y = 3 (y is already solve for) (0, 3) x y = 3

Find the x- and y-intercepts Ex4: x = -4 ***Special case*** 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! x = -4

Interpreting x-and y-intercepts: Swimming Pool x-int: (14, 0): After 14 hours, the water has a volume of 0 gallons, or the pool is completely drained. y-int: (0, 10,080): The pool contained 10,080 gallons of water at time 0, or before it started to drain. Draining a Pool Time (h) x Volume (gal) y 10,080 2 8,640 6 5,760 10 2,880 12 1,440 14

SWBAT… find x- and y-intercepts graphically and algebraically Fri, 11/30 SWBAT… find x- and y-intercepts graphically and algebraically Agenda Warm-Up (5 min) 5 MC examples (10 min) Review HW#3 (10 min) x- and y-intercepts interpretation (20 min) Warm-Up: 1. Which is the best estimate for the x-intercept of the graph of the linear function A. Between 0 and 1 B. Between 2 and 3 C. Between 1 and 2 D. Between 3 and 4 HW#4: x- and y-intercepts x y 5 1 3 2 -1 4 -3

What is the x-intercept of 3x – 4y = 24? (-6, 0) (8, 0) (0, -4) (8, -6) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

What is the y-intercept of -x + 2y = 8? (-1, 0) (-8, 0) (0, 2) (0, 4) Solve for y: Ax + By = C 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

What is the x-intercept of y = 1? (Hint: Draw this graph) (1, 0) (-1, 0) (0, 1) None x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

What is the y-intercept of y = 1? (Hint: Draw this graph) (1, 0) (-1, 0) (0, 1) None x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

What is the y-intercept of x = 3? (Hint: Draw this graph) (3, 0) (-3, 0) (0, 3) None x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

HW#4 Answers x-int = (3, 0) y-int = (0, 5) x-int = (7, 0)