Coordinate Graph | Coordinate Geometry Free PDF . A coordinate plane is a 2-dimensional plane that is formed from the intersection of a horizontal and vertical line, called the y-axis. These lines are perpendicular and intersect at zero. This point is known as the origin. Each section is called quadrant.

**A Linear Relationship**

Below is a function table that shows five ordered pairs’ x and y-coordinates. The relationship between the x and y-coordinates can be described with the following rule: The x_-coordinate plus 2 equals the y_-coordinate. This relationship can be described with the algebraic equation x + 2, , and.

**x-coordinate **

- x + 2 = you
- y-coordinate
- ordered couple
- 0
- 0 + 2 = 2
- 2
- (0,2)
- 1
- 1 + 2 = 3
- 3
- (1,3)
- 2
- 2 + 2 = 4
- 4
- (2,4)
- 3
- 3 + 2 = 5
- 5
- (3,5)
- 4
- 4 + 2 = 6
- 6
- (4,6)

The equation x +2 = y can be graphed by placing each pair on a coordinate grid. After that, the points will be connected. The graph is actually a straight line. The arrows indicate that it runs in both directions.

**The Concept:**

**Find and graph points for linear relationships**

Although your students may have already encountered ordered pairs last year it is a good idea for them to review how to find a point on the grid using an ordered pair. It will be a good day spent plotting coordinates in straight lines.

Standard: Graph points on the coordinate plan. (5.G.A.1) Materials: poster paper, or a way for class members to see a coordinate grid; straightedge

Preparation Draw large coordinate grids that can be seen by the entire class. The x and _y-axes should be labeled from 0 to 10. Prerequisite Skills & Concepts: Students need to be familiar with ordered pairs and how to locate points on a grid. These ordered pairs should be written so that all students can see them. Point to the ordered pair .

Ask Which rule describes the relationship between numbers in an ordered pair? Although there are many rules that work for this pair, students should learn this rule: The first number minus two equals and is the second.

**Ask Does this rule apply to other ordered pairs?**

This rule should be observed by students. This rule can be used to help students write each ordered pair of pairs as an equation. 6 – 2 = 4, 7- 2 = 5, 8, – 2 = 6, 9- 2 = 7.

Say: Now let’s find these ordered pairs on a grid. Ask Where would you find the point for (6.4) on the grid.

Students should state that they will “start at 0, move 6 units left, then 4 units right.” This point should be marked on the grid so that the class can see.

Students should be able to verbally explain how they will locate the point for each pair. Mark each point on your grid. It is important to move right the first number in an ordered pair, and up the second number.

**Ask Which figure will you get by connecting the grid points?**

The students should be able to see how a line is formed. Connect the points using a straightedge. Students can be provided with examples of ordered pairs that conform to a particular rule. Students should identify the rule and show how to graph it. An example of this could be: “Rule: The first plus three equals two; ordered pairs: (2.5), (3.6), (4.7), and (5.8). “

**The Conceptualization**

Find and graph points for linear relationships. Students will see the relationship between equations, straight-line graphs, and coordinate grids at this level.

**Standard: Interpret an equation as a line function.**

Materials -Poster Paper or a way for a class to display a grid public ally; straightedge; one copy each of a grid, a straightedge and lined paper

Preparation Draw a coordinate grid so that all students can see it. The x and _y_axes between 0 and 10 should be labeled. Make sure all students have a copy.

Prerequisite Skills & Concepts: Students need to be able to locate points on a grid and identify ordered pairs. Students should be able recognize and interpret equations.

**For the class to see, write the equation x+ 5 = y publically.**

**Ask What is the best way to express this equation in words?**

Students will need to explain that an equation is “a number plus five equals another,” or something similar. Draw a table that has four columns and five rows. Students should draw their own table. The first column x should be labeled, followed by the second x + 5 and the third y. For now, leave the fourth column empty. In the first column below , write “1”.

Ask How does the equation change if x is replaced with 1? Students should be able to explain the equation 1 + 5. In the second column, write “1 + 5″ below ” x + 5. In the third column, write “6” below y. Continue to replace x by 2, 3, and then 4. Students should complete the first three columns on their tables independently. Next, ask for volunteers to help you complete the table in public for your class.

Say, “Let’s write ordered pair using the values x and y.” The fourth column in your table should be called “Ordered pairs”. Students should be reminded that they move on the grid from the x-axis to the y-axis when they find points. The x first number in an ordered pair represents and the y second number represent y. These numbers are the x-, and y_-coordinates.

Ask Which number did you use for x? (1) Which number did we use for y?(6) Now, which is the first pair of ordered pairs? (1),6, Students should complete their tables. Record the completed tables in public for the class. Write Now, we will graph the equation x+5 = y on the grid. This grid is known as a coordinate grid. Let’s have a closer look at each part of the grid.

Point to the horizontal line of the grid. Say: The x-axis is the line. Point to the vertical line of the grid.

**Ask: How do you believe this line is named?** Coordinate Geometry Free PDF

- Students should understand the connection between the and-axes.
- Speak: Now let’s find the ordered pairs on this grid. Who can find (1.6 )?

Ask a volunteer to describe the location of each ordered pair. All students can see the coordinate grid and mark the exact location. Next, have students find the remaining ordered pairs using their grids.

** Speak: Let’s connect all the points. Which figure did you get?**

Coordinate Geometry Free PDF – Students should use a straight edge for connecting the points. Students can demonstrate to them how you extend both ends of the line slightly and draw arrows. This will show that the line continues in both directions. The figure should be identified by students as a straight line. Students should repeat the activity using the equation x + 2 = y. For x, use the numbers 5, 6, 7, 8 and 9.

**CONCLUSION** – **Assessment Hints and Wrap-Up**

Coordinate Geometry Free PDF . This skill will require a lot of practice. Students should be reminded to take care of their graphs and work hard. You should keep students’ progress in mind when assessing their progress. Make sure they are able to complete each step without being rushed.

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