Transcript Chapter Three 3.3

Section 3.3
More Graphing of
Lines
Copyright © 2013 Pearson Education, Inc.
Finding Intercepts
Page 178
The y-intercept is where the graph intersects the y-axis.
The x-intercept is where the graph intersects the x-axis.
Finding x – intercept
Page 179
An x-intercept of a graph is the x-coordinate of a point
where the graph intersects the x-axis. The y-coordinate of the xintercept is always zero.
The graph of y = 4x – 8 crosses the x-axis at (2, 0) and that
point is the x-intercept.
(2, 0)
Finding y- intercept
Page 179
The y-intercept of a graph is the y-coordinate of a point where
the graph intersects the y-axis. The x-coordinate of the y-intercept
is always zero.
The graph of y = 3x + 4 crosses the y-axis at (0, 4) and that
point is the y-intercept.
(0, 4)
Example
Page 180
Use intercepts to graph 3x – 4y = 12.
Solution
The x-intercept is found
by letting y = 0.
The y-intercept is found
by letting x = 0.
3 x  4 y  12
3x  4 y  12
3x  4(0)  12
3(0)  4 y  12
3 x  12
x4
4 y  12
x  3
(4, 0)
The graph passes through the
two points (4, 0) and (0, –3).
(0, 3)
Example
Page 180
Complete the table for the graph of the equation
x – y = 3.
Solution
Find corresponding values for the intercepts.
Select one more point for the check point.
X
Y
(x,y)
0
3
(0,3)
(3,0)
(1,2)
3 0
1 2
x y 3
0 y 3
y  3
y  3
x y 3
x0 3
x3
x y 3
1 y  3
y  2
y  2
The x-intercept is (3, 0). The y-intercept is (0, –3).
Graphing Using Intercepts
Page 180
Graph 2x + 3y = 6.
Graph the equation by drawing a line through the intercepts and
checkpoint.
2 x  3  ( 0)  6
x3
2  (0)  3 y  6
y2
2  (3)  3 y  6
y4
X
Y
(x,y)
3
0
(3,0)
0
2
(0,2)
-3
4
(-3,4)
6
-2
(6,-2)
2  (6)  3 y  6
y  2
Graphing Using Intercepts
Page 180
Graph x + 3y = 0.
Graph the equation by drawing a line through the intercepts and
checkpoint.
x  3  (0)  0
x0
1 (0)  3 y  0
y0
1 (3)  3 y  0
y  1
X
Y
(x,y)
0
0
(0,0)
0
0
(0,0)
3
-1
(3,-1)
-3
1
(-3,1)
Goes
through
the origin
1 (3)  3 y  0
y 1
Example
Page 181
A toy rocket is shot vertically into the air. Its velocity v in
feet per second after t seconds is given by
v = 320 – 32t. Assume that t ≥ 0 and t ≤ 10.
a. Graph the equation by finding the intercepts.
b. Interpret each intercept.
Solution
v  320  32t
a. Find the intercepts.
v  320  32t
v  320  32(0)
v  320
0  320  32t
320  32t
t  10
b. The t-intercept indicates that the rocket had a velocity of 0 feet per
second after 10 seconds. The v-intercept indicates that the rocket’s
initial velocity was 320 feet per second.
Horizontal Lines
Page 181
The equation of a horizontal line with y-intercept b
is y = b.
Example
Page 182
Graph the equation y = 2 and identify its y-intercept.
Solution
The graph of y = 2 is a horizontal line passing through the
point (0, 2), as shown below.
The y-intercept is 2.
Vertical Lines
Page 183
The equation of a vertical line with x-intercept k is x = k.
Example
Page 183
Graph the equation x = 2, and identify its x-intercept.
Solution
The graph of x = 2 is a vertical line passing through the
point (2, 0), as shown below.
The x-intercept is 2.
Example
Page 184
Write the equation of the line shown in each graph.
a.
b.
Solution
a. The graph is a horizontal line.
The equation is y = –1.
b.
The graph is a vertical line.
The equation is x = –1.
DONE
Objectives
•
Finding Intercepts
•
Horizontal Lines
•
Vertical Lines
Example
Page 184
Find an equation for a line satisfying the given conditions.
a. Vertical, passing through (3, 4).
b. Horizontal, passing through (1, 2).
c. Perpendicular to x = 2, passing through (1, 2).
Solution
c. A line perpendicular to
a. The x-intercept is 3.
x = 2 is a horizontal line
The equation is x = 3.
with y-intercept –2.
The equation is y = 2.
b. The y-intercept is 2.
The equation is y = 2.
Example
Page 180
Complete the table. Then determine the x-intercept and
y-intercept for the graph of the equation x – y = 3.
Solution
Find corresponding values of y for the given values of x.
x
3
1
0
1
y
x y 3
3  y  3
y  6
y  6
x y 3
1  y  3
y  4
y  4
3
x
3
1
0
1
3
y
6
4
3
2
0
x y 3
0 y 3
y  3
y  3
x y 3
1 y  3
y  2
y  2
x y 3
3 y  3
y  0
y0
The x-intercept is (3, 0). The y-intercept is (0, –3).
Example
Page 180
Complete the table for the graph of the equation
x – y = 3.
Solution
Find corresponding values for the intercepts.
Select one more point for the check point.
X
Y
(x,y)
0
3
(0,3)
(3,0)
(1,2)
3 0
1 2
x
3
1
0
1
3
y
6
4
3
2
0
The x-intercept is (3, 0). The y-intercept is (0, –3).