Download Graphing Linear Equations Graph Linear Equations

3-f
PERIOD
DATE
NAME
Study Guide and Intervention
Graphing Linear Equations
Identify Linear Equations and Intercepts
A linear equation i s a n e q u a t i o n t h a t
c a n b e w r i t t e n i n t h e f o r m Ax + By = C. T h i s i s c a l l e d t h e s t a n d a r d form o f a l i n e a r
equation.
Ax + By = C, where A > 0, A and B are not both zero, and A, B, and
C are integers with a greatest common factor of 1
Standard Form of a Linear Equation
Determine whether y = 6 — 3 x
i s a linear equation. Write the equation i n
s t a n d a r d form.
First rewrite the equation soboth variables are o n
t h e s a m e side o ft h e equation.
y = 6 — 3x
y + 3x = 6 — 3x + 3x
3x + y = 6
Original equation
Add 3x to each side.
Simplify.
Determine
w h e t h e r 3 x y + y = 4: + 2 x i s a
linear equation. Write the
e q u a t i o n i n s t a n d a r d form.
S i n c e t h e t e r m 3xy h a s t w o v a r i a b l e s ,
the equation cannot bew r i t t e n i n the
f o r m Ax + By = C. T h e r e f o r e , t h i s i s
not a linear equation.
The equation isnow i n standard form, with A =3,
B = I and C = 6.T h i s i sa linear equation.
Exercises
D e t e r m i n e w h e t h e r e a c h e q u a t i o n i s a l i n e a r e q u a t i o n . W r i t e yes o r n o . I f y e s ,
w r i t e t h e e q u a t i o n i n s t a n d a r d form.
=- 1
1 . 2x = 4y
2. 6 + y = 8
3.4x-2y
4. 3xy + 8^ Ay
5.3X-4 - 12
6 . y =x2 + 7
7 . y - 4 x = 9
8.
9 . -2x + 3 = 4 y
X
+ 8= 0
1 0 . 2 + | x = y
ll.^y
13. 6x + 4 y- 3 = 0
14.yx-2 = 8
1 6 . ^x - 1 2 y = 1
17. 3 +
Chapter 3
=
X
1 2 - 4 x
+
12. 3xy - y = 8
15.6x-2y
= 0
35
=
8+y
1 8 . x2 = 2 x j '
Glencoe Algebra 1
NAME
DATE
3-1
PERIOD
Study Guide and intervention
(continued)
Graphing Linear Equations
Graph Linear Equations T h e g r a p h o f a h n e a r e q u a t i o n s r e p r e s e n t s a l l t h e s o l u t i o n s o f
t h e equation. A n x-coordinate o f t h e p o i n t a t w h i c h a g r a p h o fa n e q u a t i o n crosses t h e x-axis
i n a n jc-intercept. A y - c o o r d i n a t e o f t h e p o i n t a t w h i c h a g r a p h c r o s s e s t h e y - a x i s i s c a l l e d a
y-intercept.
G r a p h 3 x + 2y = 6
by u s i n g t h e x - a n d y - i n t e r c e p t s .
T o find t h e x - i n t e r c e p t , l e t y = 0 a n d
solve for x. T h e x-intercept i s 2. T h e
graph intersects t h e x-axis a t(2, 0).
T o find t h e y - i n t e r c e p t , l e t x = 0 a n d
solve fory .
T h e j - i n t e r c e p t i s 3.T h e g r a p h
intersects t h e y-axis a t(0, 3).
Plot t h e points (2, 0) a n d (0, 3 ) a n d
draw the line through them.
y\
(0,3
o
(2, 0)
G r a p h y - 2af = 1 by making
a table.
S o l v e t h e e q u a t i o n f o r y.
y-2x
= l
y -2x + 2x = l + 2x
y = 2x + l
Original equation
Add 2x to each side.
Simplify.
S e l e c t five v a l u e s f o r t h e d o m a i n a n d m a k e a t a b l e .
T h e n graph the ordered pairs a n d draw a line
through t h e points.
X
2x + A
y
(X,/)
- 2 2(-2) + 1 - 3 (-2, - 3 )
- 1 2(-1) + 1 - 1 ( - 1 . - 1 )
0 2(0) + 1
1
(0,1)
3
1 2(1)+ 1
(1,3)
2 2(2) + 1
5
(2, 5)
X
Exercises
G r a p h each equation b y using the x - a n d y-intercepts.
1.2x
+ y = -2
2.3x- 6y= - 3
3 . -2x+y
=- 2
G r a p h e a c h e q u a t i o n b y m a k i n g a table.
4.y = 2x
Chapter 3
5 . x — 3 ' = —!
36
6.
X +
2y= 4
Glencoe Algebra 1