Graphs (a) Cartesian Plane: Constructing Cartesian Plane; Coordinate/Ordered Pair; Choosing Scales; Plotting Points on a Cartesian Plane
Subject : Mathematics
Class : JSS 2
Term : Second Term
Week : Week 10
Topic :
Graphs
- Cartesian Plane:
- Constructing Cartesian Plane;
- Coordinate/Ordered Pair;
Choosing Scales; - Plotting Points on a Cartesian Plane
- Graphs of Linear Equations
- Plotting Graphs from a Table of
Values
Previous Lesson :
Geometry : Solid Shapes (Cubes, cuboids ,cylinders, cones, capacities)
Objective: Students will be able to understand the Cartesian Plane, plot points on the plane, understand linear equations, and graph linear equations.
Materials Needed:
- Whiteboard or chalkboard
- Markers or chalk
- Printed Cartesian Plane worksheets
- Rulers
- Graph paper or Graph Book
- Pencils
- Online Materials
Content :
Graphs : Cartesian Plane
The Cartesian Plane is a graph that is made up of two number lines that intersect each other at a right angle. One number line is horizontal and the other is vertical. The point where they intersect is called the origin.
The horizontal line is called the x-axis and the vertical line is called the y-axis. The point where the x-axis and y-axis meet is called the origin, and it has coordinates (0,0).
Each point on the Cartesian Plane is represented by a pair of numbers, which are called coordinates. The first number tells you how far to move along the x-axis (left or right) and the second number tells you how far to move along the y-axis (up or down). The coordinates of a point are always written in the order (x,y).
Here is an example of a point on the Cartesian Plane: (3,5). To plot this point, you would start at the origin and move 3 units to the right on the x-axis and 5 units up on the y-axis. This would bring you to the point (3,5).
Here are some more examples:
- The point (-2,4) is two units to the left of the origin and four units up.
- The point (0,-3) is on the y-axis, three units down from the origin.
- The point (5,0) is on the x-axis, five units to the right of the origin.
The Cartesian Plane is used to graph many types of data, such as points, lines, and curves. It is an important tool in math and science, and is often used in fields like engineering and physics
Constructing Cartesian Plane; Coordinate/Ordered Pair; Choosing Scales;
Constructing a Cartesian Plane: To construct a Cartesian Plane, you need to draw two perpendicular number lines that intersect at a point, which is called the origin. One line represents the horizontal axis, which is called the x-axis, and the other line represents the vertical axis, which is called the y-axis. You can label each axis with numbers that increase or decrease as you move away from the origin.
Here is an example of a Cartesian Plane:
Coordinate/Ordered Pair: A coordinate, also called an ordered pair, is a pair of numbers that gives the location of a point on the Cartesian Plane. The first number in the ordered pair represents the x-coordinate, which tells you how far the point is from the origin along the x-axis. The second number represents the y-coordinate, which tells you how far the point is from the origin along the y-axis.
For example, the point (2,3) represents a point that is 2 units to the right of the origin and 3 units up from the origin.
Choosing Scales: When you are drawing a graph on a Cartesian Plane, it is important to choose appropriate scales for the x-axis and y-axis. The scale determines how many units on the graph correspond to each unit in real life.
For example, if you are graphing the heights of plants, you might choose a scale of 1 unit on the graph equals 10 centimeters in real life. This means that a plant that is 50 centimeters tall would be plotted at the point (0,5) on the graph.
Choosing appropriate scales can help make your graph easier to read and understand
Plotting Points on a Cartesian Plane
How to plot points on a Cartesian Plane using examples.
Plotting Points: To plot a point on a Cartesian Plane, you need to know its coordinates. Coordinates are written as an ordered pair (x,y), where x is the distance from the origin along the x-axis, and y is the distance from the origin along the y-axis.
For example, the point (2,3) has an x-coordinate of 2 and a y-coordinate of 3. To plot this point on a Cartesian Plane, you would start at the origin (which is always at the point (0,0)), move 2 units to the right along the x-axis, and then move 3 units up along the y-axis. This will bring you to the point (2,3).
Here is an example of how to plot the point (2,3) on a Cartesian Plane:
Another example is the point (-1,4). To plot this point, you would start at the origin, move 1 unit to the left along the x-axis, and then move 4 units up along the y-axis. This will bring you to the point (-1,4).
Here is an example of how to plot the point (-1,4) on a Cartesian Plane:
You can plot as many points as you need on a Cartesian Plane to create a graph. Plotting points is an important skill in math, and is used in many different areas such as physics, engineering, and statistics.
The graphs of linear equations and plotting graphs from a table of values.
(a) Graphs of Linear Equations: A linear equation is an equation whose graph is a straight line. Linear equations can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept (where the line crosses the y-axis).
To graph a linear equation, you can start by finding the y-intercept, which is the point where the line crosses the y-axis. Then, use the slope to find a second point on the line. You can do this by using the slope to rise (move up or down) and run (move left or right) from the y-intercept.
For example, the equation y = 2x + 3 represents a line with a slope of 2 and a y-intercept of 3. To graph this line, you would start at the point (0,3), which is the y-intercept. Then, you would use the slope of 2 to rise 2 units and run 1 unit to the right from the y-intercept. This would bring you to the point (1,5). You can continue to find more points on the line using the same method, or you can use a ruler to draw a straight line through the two points you already found.
Here is an example of the graph of the linear equation y = 2x + 3:
Plotting Graphs from a Table of Values:
Another way to graph a linear equation is to use a table of values. A table of values is a list of input and output values for a function or equation. For a linear equation, you can choose some values for x and then use the equation to find the corresponding values for y.
For example, let’s say you want to graph the equation y = -3x + 4. You could choose some values for x, such as -2, -1, 0, 1, and 2. Then, you can use the equation to find the corresponding values for y:
Once you have a table of values, you can plot the points on a Cartesian Plane and draw a line through them. Here is an example of how to plot the graph of
y = -3x + 4 using a table of values:
As you can see, the points from the table of values are plotted on the graph and a straight line is drawn through them. This is the graph of the linear equation y = -3x + 4.
Evaluation
- Which of the following best describes the Cartesian Plane? a) a shape b) a type of graph c) a type of measurement d) a type of calculation
Answer: b) a type of graph
- What is the origin of the Cartesian Plane? a) the first point you plot on the graph b) the point where the x-axis and y-axis intersect c) the point where the x-axis and y-axis are perpendicular d) the highest point on the graph
Answer: b) the point where the x-axis and y-axis intersect
- Which of the following is an example of an ordered pair? a) (2,3) b) 2 + 3 c) 2 x 3 d) 2 – 3
Answer: a) (2,3)
- How do you plot a point on a Cartesian Plane? a) by choosing a random location b) by using the x and y coordinates c) by counting how many lines intersect at the point d) by guessing the location
Answer: b) by using the x and y coordinates
- What is the slope of a linear equation? a) the y-intercept b) the point where the line crosses the x-axis c) the steepness of the line d) the point where the line crosses the y-axis
Answer: c) the steepness of the line
- Which of the following is an example of a linear equation? a) y = x^2 + 1 b) y = 3x – 2 c) y = 1/x d) y = sqrt(x)
Answer: b) y = 3x – 2
- How do you find the y-intercept of a linear equation? a) by finding the point where the line crosses the y-axis b) by finding the point where the line crosses the x-axis c) by finding the slope of the line d) by finding the coordinates of two points on the line
Answer: a) by finding the point where the line crosses the y-axis
- Which of the following is an example of plotting a graph from a table of values? a) using a ruler to draw a line between two points b) finding the slope of a line c) choosing appropriate scales for the axes d) plotting points using a table of input and output values
Answer: d) plotting points using a table of input and output values
- What is a table of values? a) a list of input and output values for a function or equation b) a list of coordinates for a point c) a list of numbers to plot on a graph d) a list of ordered pairs
Answer: a) a list of input and output values for a function or equation
- What is the purpose of choosing appropriate scales for a graph? a) to make the graph look pretty b) to make the graph easier to read and understand c) to make the graph larger d) to make the graph smaller
Answer: b) to make the graph easier to read and understand
Lesson Presentation
Introduction (5 minutes):
- Begin by asking students if they have ever heard of the Cartesian Plane or graphing before.
- Explain that today’s lesson will be all about the Cartesian Plane, linear equations, and graphs.
- Write down the objective of the lesson on the board.
Part 1: The Cartesian Plane (10 minutes):
- Explain what the Cartesian Plane is and what it looks like.
- Draw an example of a Cartesian Plane on the board and label the x-axis, y-axis, and the origin.
- Give examples of points and ordered pairs on the plane.
- Hand out printed Cartesian Plane worksheets and have students practice plotting points on the plane.
Part 2: Linear Equations (15 minutes):
- Define what a linear equation is and how to write it in slope-intercept form.
- Explain what slope and y-intercept mean and how to find them.
- Give examples of linear equations and how to graph them on the Cartesian Plane.
- Hand out graph paper and have students practice graphing linear equations.
Part 3: Plotting Graphs from a Table of Values (10 minutes):
- Explain how to plot a graph from a table of values.
- Provide an example of a table of values and have students practice plotting the points on the Cartesian Plane.
- Have students connect the plotted points to make a line.
Assessment Test
- The Cartesian Plane is a type of __________. Answer: graph
- The origin of the Cartesian Plane is where the x-axis and y-axis __________. Answer: intersect
- An ordered pair consists of two __________ separated by a comma. Answer: numbers
- To plot a point on the Cartesian Plane, you need to know its __________ and __________ coordinates. Answer: x and y
- The slope of a linear equation determines its __________. Answer: steepness
- To find the y-intercept of a linear equation, you need to find the point where the line crosses the __________. Answer: y-axis
- A table of values is a list of __________ and __________ values for a function or equation. Answer: input and output
- To graph a linear equation, you can use the __________ and __________ values from a table of values. Answer: x and y
- Choosing appropriate scales for the axes is important in making a graph easy to read and __________. Answer: understand
- To graph a linear equation, you need to plot at least __________ points on the Cartesian Plane. Answer: two
Part 4: Assessment (10-20 minutes):
- Have students complete a worksheet that includes plotting points on the Cartesian Plane, graphing linear equations, and plotting graphs from a table of values.
- Collect the worksheets and review them to see how well students understood the lesson.
Conclusion (5 minutes):
- Review the objective of the lesson and ask students if they feel they accomplished it.
- Answer any remaining questions students may have about the Cartesian Plane, linear equations, or graphing.
- Assign any homework if necessary
Weekly Assessment
- What is the Cartesian Plane? a) a shape b) a type of graph c) a type of measurement d) a type of calculation Answer: b) a type of graph
- What is the origin of the Cartesian Plane? a) the first point you plot on the graph b) the point where the x-axis and y-axis intersect c) the point where the x-axis and y-axis are perpendicular d) the highest point on the graph Answer: b) the point where the x-axis and y-axis intersect
- What is an ordered pair? a) a pair of shoes b) a pair of numbers that gives the location of a point on the Cartesian Plane c) a pair of gloves d) a pair of scissors Answer: b) a pair of numbers that gives the location of a point on the Cartesian Plane
- How do you plot a point on a Cartesian Plane? a) by choosing a random location b) by using the x and y coordinates c) by counting how many lines intersect at the point d) by guessing the location Answer: b) by using the x and y coordinates
- What is the slope of a linear equation? a) the y-intercept b) the point where the line crosses the x-axis c) the steepness of the line d) the point where the line crosses the y-axis Answer: c) the steepness of the line
- Which of the following is an example of a linear equation? a) y = x^2 + 1 b) y = 3x – 2 c) y = 1/x d) y = sqrt(x) Answer: b) y = 3x – 2
- How do you find the y-intercept of a linear equation? a) by finding the point where the line crosses the y-axis b) by finding the point where the line crosses the x-axis c) by finding the slope of the line d) by finding the coordinates of two points on the line Answer: a) by finding the point where the line crosses the y-axis
- What is a table of values? a) a list of input and output values for a function or equation b) a list of coordinates for a point c) a list of numbers to plot on a graph d) a list of ordered pairs Answer: a) a list of input and output values for a function or equation
- What is the purpose of choosing appropriate scales for a graph? a) to make the graph look pretty b) to make the graph easier to read and understand c) to make the graph larger d) to make the graph smaller Answer: b) to make the graph easier to read and understand
- Which of the following is an example of plotting a graph from a table of values? a) using a ruler to draw a line between two points b) finding the slope of a line c) choosing appropriate scales for the axes d) plotting points using a table of input and output values Answer: d) plotting points using a table of input and output values