Transcript Intercepts - Goshen Algebra

LOT
 Please make sure that you have your
 Binder
 Journal
 Also grab the small paper on the front
table and begin working
 If on ALEKS, please start working
M. Pickens 2006
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Intercepts
M. Pickens 2006
Objectives
 SWBAT find x and y-intercepts given a
graph
 SWBAT find x and y-intercepts given an
equation
 SWBAT use x and y-intercepts to sketch
a graph
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What does it mean to INTERCEPT a
pass in football?
The path of the defender crosses the
path of the thrown football.
IN YOUR JOURNAL!!!
In algebra, what do you think
x- and y-intercepts are? M. Pickens 2006
What are intercepts?
 An intercept is where something
intersects or touches
 For example,
 an x-intercept is where the graph touches
the x-axis
 a y-intercept is where the graph touches
the y-axis
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Intercepts of a Graph
y
 What are the x-
intercept and yintercept of the
graph at right?
 X-intercept:
(5, 0)
 Y-intercept:
(0, 7)
(0, 7)
x
(5, 0)
Where
Where itit touches
touches the
the y-axis
x-axis
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Intercepts of a Graph
y
 What are the x-
intercept and yintercept of the
graph at right?
 X-intercept: (-8,
 Y-intercept: (0,
(0, 6)
0)
6)
x
(-8, 0)
Where
Where itit touches
touches the
the y-axis
x-axis
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Intercepts of a Graph
 What are the x and y-intercepts of the graphs below?
Notice:
For all the
x-intercepts the
y-coordinate is ____
0
For all the
y-intercepts the
0
x-coordinate is ____
X-intercept:
Y-intercept:
(3, 0)
X-intercept:
(-9, 0)
Y-intercept:
(0, -5)
(0, -8)
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Which are which?
 Which of the coordinates below are x-intercepts?
T, V, W, X
 Which of the coordinates below are y-intercepts?
S, U, W, Y
 Which of the coordinates are neither? Why???
R, Z
R(3, 5)
S(0, 9)
T(-2, 0)
U(0, 1)
V(15, 0)
W(0, 0)
X( ½ , 0) Y(0, 8)
Z(1, 0.5)
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Objective
 SWBAT find x and y-intercepts given a
graph
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Intercepts of an Equation
 We know for an x-intercept the
______________
Y-coordinate is 0
x-coordinate is 0
 In the y-intercept the ___________
 We can use this to solve equations.
 To
solve for an x-intercept substitute in a 0
for y.
 To solve for a y-intercept substitute in a 0
for x.
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Intercepts of an Equation
 Find the x and y-intercepts of the
equation -2x + 3y = 18
To find the y-intercept
To find the x-intercept
x
substitute in 0 for _____
y
substitute in 0 for _____
-2x + 3y = 18
-2x + 3(0) = 18
-2x + 0 = 18
-2x = 18
-2
-2
-2x + 3y = 18
-2(0) + 3y = 18
0 + 3y = 18
3y = 18
3
3
x = -9
y=6
( -9, 0)
( 0, 6)
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Intercepts of an Equation
 Find the x and y-intercepts of the equation
y  4 x  16
y
To find the x-intercept substitute in 0 for _____
y  4 x  16
0  4 x  16
- 16
-16
To find the y-intercept
x
substitute in 0 for _____
y  4 x  16
16  4x
y  4(0)  16
-4
-4
4=x
x=4
y  0  16
(4, 0)
y = 16
(0, 16)
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Find the x- and y-intercepts.
3. y = 7
***Special case***
x-intercept: Substitute in 0 for y.
Does 0 = 7?
No! There is no x-intercept. None
What type of lines have no x-intercept?
Horizontal!
Horizontal lines…y = 7…y-int = (0, 7)
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What is the y-intercept of
x = 3?
1. (3, 0)
2. (-3, 0)
3. (0, 3)
4. None
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Objective
 SWBAT find x and y-intercepts given an
equation
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Sketching a Graph from Intercepts
 Find the intercept of the equation -3x + 2y =12
and sketch the graph
X-intercept: (substitute in 0 for y)
-3x + 2(0) = 12
-3x = 12
(-4, 0)
x = -4
Y-intercept: (substitute in 0 for x)
-3(0) + 2y = 12
0 + 2y = 12
(0, 6)
y=6
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Sketching a Graph from Intercepts
 Find the intercept of the equation 5 x  3 y  15
and sketch the graph
X-intercept: (substitute in 0 for y)
5 x  3(0)  15
5x – 0 = 15
5x = 15
5
5
x=3
(3, 0)
Y-intercept: (substitute in 0 for x)
5(0)  3 y  15
0 – 3y = 15
-3y = 15
-3
-3
y = -5
(0, -5)
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Conclusion
something intersects or touches
 Intercept is : Where
_____________________
 The x-intercept is _________________
Where it touches the x-axis
Where it touches the y-axis
 The y-intercept is _________________
 To find the x-intercept of an equation
substitute in 0 for Y
____________________
 To find the y-intercept of an equation
substitute in 0 for X
____________________
M. Pickens 2006
Objectives
 SWBAT find x and y-intercepts given a
graph
 SWBAT find x and y-intercepts from an
equation
 SWBAT use x and y-intercepts to sketch
a graph
M. Pickens 2006