3 Title

Beginning Algebra
Tutorial 20: 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

 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)

 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