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Graph ordered pairs from patterns

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5509965
The table shows corresponding terms from two number patterns. Use Pattern A as the x-coordinate and Pattern B as the y-coordinate. Write the four ordered pairs. <table><tr><th>Position</th><th>Pattern A</th><th>Pattern B</th></tr><tr><td>1</td><td>\(1\)</td><td>\(2\)</td></tr><tr><td>2</td><td>\(3\)</td><td>\(5\)</td></tr><tr><td>3</td><td>\(5\)</td><td>\(8\)</td></tr><tr><td>4</td><td>\(7\)</td><td>\(11\)</td></tr></table>

Hints

- An ordered pair is written as \((x, y)\). - Use the Pattern A entry in a row as the first coordinate. - Use the Pattern B entry from the same row as the second coordinate.

Solution

1. Pair the terms in each row with Pattern A first and Pattern B second. 2. The ordered pairs are \((1, 2)\), \((3, 5)\), \((5, 8)\), and \((7, 11)\).

Answer

\((1, 2)\), \((3, 5)\), \((5, 8)\), \((7, 11)\)
5509975
Pattern A starts at \(1\) and follows the rule “add \(2\).” Pattern B starts at \(2\) and follows the rule “add \(3\).” The graph shows the first two ordered pairs \((\text{Pattern A}, \text{Pattern B})\). What ordered pair should be plotted next?
Figure for problem 550997

Hints

- Extend each pattern one position beyond the two points already shown. - Use the next Pattern A term as the x-coordinate. - Use the corresponding Pattern B term as the y-coordinate.

Solution

1. The next Pattern A term after \(3\) is \(5\). 2. The next Pattern B term after \(5\) is \(8\). 3. The next ordered pair is \((5, 8)\).

Answer

\((5, 8)\)
5509985
The graph shows four ordered pairs made from corresponding terms of Pattern A and Pattern B. From left to right, the points represent positions \(1\) through \(4\). Pattern A is on the x-axis and Pattern B is on the y-axis. What are the two terms at position \(3\), and what ordered pair represents them?
Figure for problem 550998

Hints

- Count the plotted points from left to right to locate position \(3\). - Read the x-coordinate from the horizontal axis and the y-coordinate from the vertical axis. - Keep Pattern A first when writing the ordered pair.

Solution

1. The third plotted point from the left is at x-coordinate \(6\) and y-coordinate \(9\). 2. Therefore, the position-\(3\) terms are \(6\) in Pattern A and \(9\) in Pattern B. 3. The ordered pair is \((6, 9)\).

Answer

Pattern A term: \(6\) Pattern B term: \(9\) Ordered pair: \((6, 9)\)
5509995
The table lists four ordered pairs made from corresponding terms of Pattern A and Pattern B. Pattern A is the x-coordinate and Pattern B is the y-coordinate. The graph shows only three of the four points. Which ordered pair from the table is missing from the graph? State where it should be plotted. <table><tr><th>Position</th><th>Pattern A</th><th>Pattern B</th></tr><tr><td>1</td><td>\(4\)</td><td>\(1\)</td></tr><tr><td>2</td><td>\(7\)</td><td>\(3\)</td></tr><tr><td>3</td><td>\(10\)</td><td>\(5\)</td></tr><tr><td>4</td><td>\(13\)</td><td>\(7\)</td></tr></table>
Figure for problem 550999

Hints

- Turn each table row into an ordered pair with Pattern A first. - Compare the four table pairs with the three points already shown on the graph. - The pair that does not appear on the graph is the one that must be plotted.

Solution

1. The table gives the ordered pairs \((4, 1)\), \((7, 3)\), \((10, 5)\), and \((13, 7)\). 2. The graph already shows \((4, 1)\), \((7, 3)\), and \((10, 5)\). 3. The missing point is \((13, 7)\), so it should be plotted at x-coordinate \(13\) and y-coordinate \(7\).

Answer

The missing ordered pair is \((13, 7)\). Plot it at x-coordinate \(13\) and y-coordinate \(7\).
5510005
Pattern A starts at \(2\) and follows the rule “add \(3\).” Pattern B starts at \(7\) and follows the rule “add \(2\).” A student plotted the first three corresponding ordered pairs, using Pattern A as x and Pattern B as y, but one point is incorrect. Identify the incorrect plotted point and give the coordinates it should have.
Figure for problem 551000

Hints

- Generate the first three terms of each pattern from the stated rules. - Pair terms from the same position with Pattern A first and Pattern B second. - Compare those expected ordered pairs with the three plotted points.

Solution

1. The first three Pattern A terms are \(2, 5, 8\), and the first three Pattern B terms are \(7, 9, 11\). 2. The correct ordered pairs are \((2, 7)\), \((5, 9)\), and \((8, 11)\). 3. The graph shows \((9, 5)\) instead of \((5, 9)\), so the coordinates of the second point were reversed.

Answer

The incorrect point is \((9, 5)\). It should be \((5, 9)\).
5510015
A school club packs snack bags. In Bag Pattern A, the number of juice boxes starts at \(4\) and increases by \(2\) for each new stage. In Bag Pattern B, the number of granola bars starts at \(6\) and increases by \(3\). The graph shows the first three corresponding ordered pairs \((\text{juice boxes}, \text{granola bars})\). a) What does the plotted point \((8, 12)\) mean in this context? b) What ordered pair should come next?
Figure for problem 551001

Hints

- Read the x-coordinate as the juice-box count and the y-coordinate as the granola-bar count. - Interpret a plotted point using both quantities from the same stage. - Extend each pattern once to determine the next ordered pair.

Solution

a) The point \((8, 12)\) means that at the third stage there are \(8\) juice boxes and \(12\) granola bars. b) The next juice-box count is \(8 + 2 = 10\), and the next granola-bar count is \(12 + 3 = 15\). The next ordered pair is \((10, 15)\).

Answer

a) At the third stage, there are \(8\) juice boxes and \(12\) granola bars. b) \((10, 15)\)
5510025
Pattern A starts at \(3\) and follows the rule “add \(4\).” Pattern B starts at \(5\) and follows the rule “add \(6\).” A student says the ordered pair \((23, 34)\) belongs to the graph of corresponding terms, with Pattern A as x and Pattern B as y. Decide whether the student is correct. If not, give the ordered pair that has x-coordinate \(23\) and justify your answer.

Hints

- Locate \(23\) in Pattern A by following its add rule. - Use the same position number in Pattern B; corresponding coordinates must come from the same position. - Check both coordinates against their pattern rules before accepting the proposed point.

Solution

1. Pattern A reaches \(23\) at the sixth position: \(3, 7, 11, 15, 19, 23\). 2. The first six Pattern B terms are \(5, 11, 17, 23, 29, 35\). 3. At the same sixth position, the corresponding Pattern B term is \(35\), not \(34\). 4. Therefore, \((23, 34)\) does not belong; the correct ordered pair with x-coordinate \(23\) is \((23, 35)\).

Answer

The student is not correct. The correct ordered pair is \((23, 35)\).

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