1. 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

2. y = 2x + 1 x

3. 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

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

5. 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

6. 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)

7. 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! 

8. 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)

9. What are the x- and y-intercepts?-3 -1 -2 1 2 3
x-int: (-2, 0)
y-int: (0, 2)

10. 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)

11. 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

12. 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, - )

13. 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

14. 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:

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

16. Do HW#1: #10 - #12

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

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