Beginning Algebra
Answer/Discussion to Practice
Problems
on The Rectangular Coordinate
System
 Answer/Discussion
to 1a
A(3, 1), B(-2, -1/2), C(2, -2), and D(0,1)
A(3, 1) lies in quadrant I.
B(-2, -1/2) lies in quadrant III.
C(2, -2) lies in quadrant IV.
D(0, 1) lies on the y axis.
(return to problem
1a) |
| Answer/Discussion
to 2a
Since point A corresponds to 4 on the x-axis
and 2 on the y-axis, then A's ordered pair
is (4, 2).
Since point B corresponds to 0 on the x-axis
and 4 on the y-axis, then B's ordered pair
is (0, 4).
Since point C corresponds to -2 on the x-axis
and 2 on the y-axis, then C's ordered pair
is (-2, 2).
Since point D corresponds to - 4 on the x-axis
and 0 on the y-axis, then D's ordered pair
is (- 4, 0).
Since point E corresponds to -2 on the x-axis
and -3 on the y-axis, then E's ordered pair
is (-2, -3).
Since point F corresponds to 3 on the x-axis
and -3 on the y-axis, then F's ordered pair
is (3, -3).
(return to problem
2a) |
| Answer/Discussion
to 3a
y = 4x
- 10 (0, -10), (1, -14), (-1, -14) |
| Let's start with the ordered pair (0, -10).
Which number is the x value and which one
is the y value? If you said x
= 0 and y = -10, you are correct!
Let's plug (0, -10) into the equation and see what we get: |
 |
*Plug in 0 for x
and -10 for y |
This is a TRUE statement, so (0, -10) is a solution to the equation
y
= 4x - 10.
Now, let's take a look at (1, -14).
Which number is the x value and which one
is the y value? If you said
x
= 1 and y = -14, you are right!
Let's plug (1, -14) into the equation and see what we get: |
 |
*Plug in 1 for x
and -14 for y
|
This is a FALSE statement, so (1, -14) is NOT a solution to the
equation y = 4x
- 10.
Now, let's take a look at (-1, -14).
Which number is the x value and which one
is the y value? If you said
x
= -1 and y = -14, you are right!
Let's plug (-1, -14) into the equation and see what we get: |
 |
*Plug in -1 for x
and -14 for y
|
| Answer/Discussion
to 3b
y = -5 ; (2, -5),
(-5, 1), (0, -5) |
| Let's start with the ordered pair (2, -5).
Which number is the x value and which one
is the y value? If you said x
= 2 and y = -5, you are correct!
Let's plug (2, -5) into the equation and see what we get: |
 |
*Plug in -5 for y |
This is a TRUE statement, so (2, -5) is a solution to the equation
y
= -5.
Now, let's take a look at (-5, 1).
Which number is the x value and which one
is the y value? If you said
x
= -5 and y = 1, you are right!
Let's plug (-5, 1) into the equation and see what we get: |
 |
*Plug in -5 for y |
This is a FALSE statement, so (-5, 1 ) is NOT a solution to the
equation y = -5.
Now, let's take a look at (0, -5).
Which number is the x value and which one
is the y value? If you said
x
= 0 and y = -5, you are right!
Let's plug (0, -5) into the equation and see what we get: |
 |
*Plug in -5 for y |
| Answer/Discussion
to 4a
 ; (0,
) and ( , 1)
|
| In the ordered pair (0, ), is 0 that is given the
x or the y value?
If you said x, you are correct.
Plugging in 0 for x into the given equation
and solving for y we get: |
 |
*Plug in 0 for x
*Solve for y
|
So, the ordered pair (0, - 4) would be a solution to the
given equation.
In the ordered pair ( , 1), is the 1 that is given the
x
or the y value?
If you said y, you are correct.
Plugging in 1 for y into the given equation
and solving for x we get: |
 |
*Plug in 1 for y
*Solve for x
|
| Answer/Discussion
to 5a
|
| Plugging in 0 for x into the given equation
and solving for y we get: |
So, the ordered pair (0, 3/2) would be a solution to the given equation.
Plugging in -1 for x into the given equation
and solving for y we get: |
| So, the ordered pair (-1, 3/2) would be another solution to the
given equation.
Plugging in 1 for x into the given equation
and solving for y we get: |
| So, the ordered pair (1, 3/2) would be another solution to the given
equation.
Filling in the table we get:
(return to problem
5a) |
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Last revised on Jan. 9, 2002 by Kim Seward. |
