Question

function tables and the coordinate plane
grade 5 geometry worksheet
complete the table below. write the corresponding ordered pairs and plot them on the coordinate plane.

rule: ( y = 2 - x )

x	y	ordered pairs
-2		( , )
-1
0
1
2

coordinate plane image

rule: ( y = 3x )

x	y	ordered pairs
-2		( , )
-1
0
1
2

coordinate plane image

Explanation:

For the rule \( y = 2 - x \):

Step 1: When \( x = -2 \)

Substitute \( x = -2 \) into \( y = 2 - x \).
\( y = 2 - (-2) = 2 + 2 = 4 \)
Ordered pair: \( (-2, 4) \)

Step 2: When \( x = -1 \)

Substitute \( x = -1 \) into \( y = 2 - x \).
\( y = 2 - (-1) = 2 + 1 = 3 \)
Ordered pair: \( (-1, 3) \)

Step 3: When \( x = 0 \)

Substitute \( x = 0 \) into \( y = 2 - x \).
\( y = 2 - 0 = 2 \)
Ordered pair: \( (0, 2) \)

Step 4: When \( x = 1 \)

Substitute \( x = 1 \) into \( y = 2 - x \).
\( y = 2 - 1 = 1 \)
Ordered pair: \( (1, 1) \)

Step 5: When \( x = 2 \)

Substitute \( x = 2 \) into \( y = 2 - x \).
\( y = 2 - 2 = 0 \)
Ordered pair: \( (2, 0) \)

For the rule \( y = 3x \):

Step 1: When \( x = -2 \)

Substitute \( x = -2 \) into \( y = 3x \).
\( y = 3\times(-2) = -6 \)
Ordered pair: \( (-2, -6) \)

Step 2: When \( x = -1 \)

Substitute \( x = -1 \) into \( y = 3x \).
\( y = 3\times(-1) = -3 \)
Ordered pair: \( (-1, -3) \)

Step 3: When \( x = 0 \)

Substitute \( x = 0 \) into \( y = 3x \).
\( y = 3\times0 = 0 \)
Ordered pair: \( (0, 0) \)

Step 4: When \( x = 1 \)

Substitute \( x = 1 \) into \( y = 3x \).
\( y = 3\times1 = 3 \)
Ordered pair: \( (1, 3) \)

Step 5: When \( x = 2 \)

Substitute \( x = 2 \) into \( y = 3x \).
\( y = 3\times2 = 6 \)
Ordered pair: \( (2, 6) \)

Filled Tables:

For \( y = 2 - x \):

\( x \)	\( y \)	Ordered Pairs
-1	3	(-1, 3)
0	2	(0, 2)
1	1	(1, 1)
2	0	(2, 0)

For \( y = 3x \):

\( x \)	\( y \)	Ordered Pairs
-1	-3	(-1, -3)
0	0	(0, 0)
1	3	(1, 3)
2	6	(2, 6)

To plot the points:

• For \( y = 2 - x \), plot the points \((-2, 4)\), \((-1, 3)\), \((0, 2)\), \((1, 1)\), \((2, 0)\) on the coordinate plane.
• For \( y = 3x \), plot the points \((-2, -6)\), \((-1, -3)\), \((0, 0)\), \((1, 3)\), \((2, 6)\) on the coordinate plane.

(Note: Plotting is a graphical task where you locate each ordered pair on the x - y coordinate system, with the first number of the ordered pair being the x - coordinate and the second number being the y - coordinate.)

Answer:

For the rule \( y = 2 - x \):

Step 1: When \( x = -2 \)

Substitute \( x = -2 \) into \( y = 2 - x \).
\( y = 2 - (-2) = 2 + 2 = 4 \)
Ordered pair: \( (-2, 4) \)

Step 2: When \( x = -1 \)

Substitute \( x = -1 \) into \( y = 2 - x \).
\( y = 2 - (-1) = 2 + 1 = 3 \)
Ordered pair: \( (-1, 3) \)

Step 3: When \( x = 0 \)

Substitute \( x = 0 \) into \( y = 2 - x \).
\( y = 2 - 0 = 2 \)
Ordered pair: \( (0, 2) \)

Step 4: When \( x = 1 \)

Substitute \( x = 1 \) into \( y = 2 - x \).
\( y = 2 - 1 = 1 \)
Ordered pair: \( (1, 1) \)

Step 5: When \( x = 2 \)

Substitute \( x = 2 \) into \( y = 2 - x \).
\( y = 2 - 2 = 0 \)
Ordered pair: \( (2, 0) \)

For the rule \( y = 3x \):

Step 1: When \( x = -2 \)

Substitute \( x = -2 \) into \( y = 3x \).
\( y = 3\times(-2) = -6 \)
Ordered pair: \( (-2, -6) \)

Step 2: When \( x = -1 \)

Substitute \( x = -1 \) into \( y = 3x \).
\( y = 3\times(-1) = -3 \)
Ordered pair: \( (-1, -3) \)

Step 3: When \( x = 0 \)

Substitute \( x = 0 \) into \( y = 3x \).
\( y = 3\times0 = 0 \)
Ordered pair: \( (0, 0) \)

Step 4: When \( x = 1 \)

Substitute \( x = 1 \) into \( y = 3x \).
\( y = 3\times1 = 3 \)
Ordered pair: \( (1, 3) \)

Step 5: When \( x = 2 \)

Substitute \( x = 2 \) into \( y = 3x \).
\( y = 3\times2 = 6 \)
Ordered pair: \( (2, 6) \)

Filled Tables:

For \( y = 2 - x \):

\( x \)	\( y \)	Ordered Pairs
-1	3	(-1, 3)
0	2	(0, 2)
1	1	(1, 1)
2	0	(2, 0)

For \( y = 3x \):

\( x \)	\( y \)	Ordered Pairs
-1	-3	(-1, -3)
0	0	(0, 0)
1	3	(1, 3)
2	6	(2, 6)

To plot the points:

• For \( y = 2 - x \), plot the points \((-2, 4)\), \((-1, 3)\), \((0, 2)\), \((1, 1)\), \((2, 0)\) on the coordinate plane.
• For \( y = 3x \), plot the points \((-2, -6)\), \((-1, -3)\), \((0, 0)\), \((1, 3)\), \((2, 6)\) on the coordinate plane.

(Note: Plotting is a graphical task where you locate each ordered pair on the x - y coordinate system, with the first number of the ordered pair being the x - coordinate and the second number being the y - coordinate.)