Beginning Algebra Tutorial 20

Beginning Algebra
Answer/Discussion to Practice Problems
Tutorial 20: The Rectangular Coordinate System

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Answer/Discussion to 1a

A(3, 1), B(-2, -1/2), C(2, -2), and D(0,1)

ad1a

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

problem 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

This is a TRUE statement, so (-1, -14) is a solution to the equation y = 4x - 10.

(return to problem 3a)

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

This is a TRUE statement, so (0, -5) is a solution to the equation y = -5.

(return to problem 3b)

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

So, the ordered pair (5, 1) would be another solution to the given equation.

(return to problem 4a)

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:

x y 0 3/2 -1 3/2 1 3/2

(return to problem 5a)

WTAMU > Virtual Math Lab >Beginning Algebra >Tutorial 20: The Rectangular Coordinate System