SWBAT… find x- and y-intercepts algebraically and graphically. Thurs, 11/4 SWBAT… find x- and y-intercepts algebraically and graphically. Agenda Warm-Up (10 min) Notes on x- and y intercepts (15 min) OYO problems (10 min) Warm-Up: Write your HW in your planners for this week Graph 2x – y = -1 using a table of values Circle and label the point where the line crosses the x-axis 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

y = 2x + 1 x

New unit - what will we be learning (4 weeks) x-and y-intercepts (solving and interpreting) Slope (solving and interpreting) Graphing and writing equations of lines Slope-intercept form  y = mx + b Point slope form  (y – y1) = m(x = x1) Standard forms  Ax + By = C Parallel and perpendicular lines Lines of best fit

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

Also called the Zero-Zero Method 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 ) Also called the Zero-Zero Method

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? Q: What was the y-intercept graphically? A: (0, 1) Q: What was the y-intercept algebraically? AHA!!! Don’t you love it when math makes sense! 

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)

What are the x- and y-intercepts? -3 -1 -2 1 2 3 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)

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

Graph 3x – 5y = 9 using x- and y-intercepts 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, - )

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

When an equation is given in the form, Ax + By = C, what is the slope: In the last two examples the equation of line was called Standard Form, Ax + By = C 2x – y = -1 3x – 5y = 9 When an equation is given in the form, Ax + By = C, what is the slope:

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

Do HW#1: #10 - #12

SWBAT… interpret x- and y-intercepts Tues, 11/22 SWBAT… interpret x- and y-intercepts Agenda Warm-Up (10 min) x- and y-intercepts; special cases (15 min) Interpreting x and y intercepts (10 min) Warm-Up: Graph 2x + 5y = -10 using x- and y-intercepts. 2. Solve for y: Ax + By = C HW#2: Interpreting x-and y-intercepts x-int., y = 0 (substitute 0 for y) (-5, 0) y-int, x = 0 (0, -2) A = -2 B = 5 m = -A/B m = 2/5

Find the x- and y-intercepts of y = 3 ***Special case*** 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! x y = 3

Find the x- and y-intercepts of 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

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