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# 2.2: Ordered Pairs

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Algebra I, Chapter 1, Lesson 6.

## Problem 1 - Ordered Pairs

1. a. For the point (2,6)\begin{align*}(-2, 6)\end{align*}, the first number, 2\begin{align*}-2\end{align*}, is the ____ -coordinate (or the abscissa).

b. For the point (2,6)\begin{align*}(-2, 6)\end{align*}, the second number, 6\begin{align*}6\end{align*}, is the ____ -coordinate (or the ordinate).

To graph a point, enter the coordinate in L1\begin{align*}L1\end{align*} and L2\begin{align*}L2\end{align*}. Then turn the Stat Plot on and display the graph.

For example, to graph (1,4)\begin{align*}(1, 4)\end{align*}, press STAT. Then enter 1\begin{align*}1\end{align*} in L1\begin{align*}L1\end{align*} and 4\begin{align*}4\end{align*} in L2\begin{align*}L2\end{align*}. Press 2nd\begin{align*}2^{nd}\end{align*} [STAT PLOT] and match the settings shown at the right. Press # and select ZStandard.

2. a. The point (1,4)\begin{align*}(1, 4)\end{align*} is in the first quadrant. In which quadrant is (1,4)\begin{align*}(1,-4)\end{align*}?

b. In which quadrant is (5,2)\begin{align*}(-5, 2)\end{align*}?

c. In which quadrant is (3,2)\begin{align*}(-3, -2)\end{align*}?

d. In which quadrant is (4,4)\begin{align*}(4, 4)\end{align*}?

e. In which quadrant is (4,0)\begin{align*}(-4, 0)\end{align*}?

f. In which quadrant is (3,5)\begin{align*}(3, 5)\end{align*}?

To explore ordered pairs, press Y=\begin{align*}Y=\end{align*} and make sure all the equations are cleared. Then, press GRAPH and use the arrow keys to move the cursor.

3. a. Where are the coordinates (negative, positive)?

b. Where are the coordinates (positive, negative)?

c. Where is the ordered pair when it is (positive, positive)?

d. Where is the ordered pair when it is (negative, negative)?

Plot the following ordered pairs on the graph at the right. Label each pair with the appropriate letter.

A(1,3)C(1,3)H(5,1)K(4,2)M(4,4)S(6,1)O(2,2)R(5,1)T(2,2)\begin{align*}& A(-1,3) && K(4,-2) && O(-2,-2) \\ & C(1,-3) && M(-4,4) && R(-5,-1) \\ & H(5,1) && S(6,-1) && T(2,2)\end{align*}

4. What phrase do the points spell?

## Problem 2 – Order Pairs

Math is everywhere. At the market, the equation y=1.5x\begin{align*}y = 1.5x\end{align*} represents the cost to buy x\begin{align*}x\end{align*} amount of pears, where y\begin{align*}y\end{align*} is the cost in dollars.

For example, you order 8\begin{align*}8\end{align*} pears. The cost is 12\begin{align*}\12\end{align*}. This can be written as the ordered pair (8,12)\begin{align*}(8, 12)\end{align*}. 5. Your order came to3\begin{align*}\3\end{align*}. How many pears did you order?

6. Enter 5\begin{align*}5\end{align*} ordered pairs for the cost of ordering pears using L1\begin{align*}L1\end{align*} and L2\begin{align*}L2\end{align*}. If data already exists, arrow up to the top of the list and press CLEAR[ENTER] to clear the data.

Create the scatter plot and record your observation.

7. Press Y=\begin{align*}Y=\end{align*}. Graph the function f(x)=x\begin{align*}f(x) = x\end{align*} in Y1\begin{align*}Y1\end{align*}. Change the slope of the function until the line matches the points. What is the slope of your line? How does it relate to the problem?

## Extension

We saw that values of a function can be written as a set of ordered pairs, listed in a table of values, and graphed as a scatter plot.

Extension 1: Find some other real-life data. Represent it as a set of ordered pairs, table, and scatter plot.

Extension 2: Come up with your own puzzle like the one at the bottom on page 1 of this worksheet. that you can share with a friend and your teacher.

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