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Cartesian Plane and Coordinate System
Introduction:
The Cartesian Plane consists of two perpendicular number lines. The vertical y-axis, and the horizontal x-axis. These two lines intersect at a point called the origin. This system establishes a correspondence between points in the plane and pairs of real numbers. For every pair of real numbers, there corresponds a point in the plane. The Cartesian Plane also consists of four quadrants. The top-right quarter is Quadrant I, the top-left is Quadrant II, the bottom-left is Quadrant III, and the bottom-right is Quadrant IV. In an ordered pair of real numbers, the y-coordinate is usually listed first while the x-coordinate comes next.
( 8 , 4 ) – In this example, 4is the y-coordinate and thus, it corresponds to the eighth point above the originwhile8 corresponds to the fourth point to the right. The corrdinates correspond to the point where the lines of these two numbers intersect.
*LAGYAN NYO NG CARTESIAN PLANE
Examples:
( 3 , 5 )
(-5 ,-4)
*LAGYAN NYO NG CARTESIAN PLANE
Questions:
Create a Cartesian Plane and plot the points of the following coordinates and label them accordingly. 1. (-2 , 5) 2. ( 6 ,-3) 3. ( 4 , 2) 4. (-4 ,-2) 5. (-3 ,-4)
System of Linear Equations in 2 variables
Review:
- Addition and Subtraction of Real Numbers
Introduction:
A system of linear equations in two variables refers to at least two linear equations with two unknowns. The objective is to find the ordered pair, which when applied to the two equations would make them both true.
Examples:
x– y = 2 (Equation 1) x + 2y = 8 (Equation 2)
If x = 4 and y = 2:
4 – 2 = 2 Substitute x and y with their corresponding values.
4 + 2(2) = 8
The substitutes make both the equations true, therefore, ( 4 , 2 ) is the correct ordered pair.
Questions:
Identify whether the ordered pair correctly corresponds with the equations. Write true or false beside each equation. 1. x + y = 10 true x = 6 x - y
Introduction:
The Cartesian Plane consists of two perpendicular number lines. The vertical y-axis, and the horizontal x-axis. These two lines intersect at a point called the origin. This system establishes a correspondence between points in the plane and pairs of real numbers. For every pair of real numbers, there corresponds a point in the plane. The Cartesian Plane also consists of four quadrants. The top-right quarter is Quadrant I, the top-left is Quadrant II, the bottom-left is Quadrant III, and the bottom-right is Quadrant IV. In an ordered pair of real numbers, the y-coordinate is usually listed first while the x-coordinate comes next.
( 8 , 4 ) – In this example, 4is the y-coordinate and thus, it corresponds to the eighth point above the originwhile8 corresponds to the fourth point to the right. The corrdinates correspond to the point where the lines of these two numbers intersect.
*LAGYAN NYO NG CARTESIAN PLANE
Examples:
( 3 , 5 )
(-5 ,-4)
*LAGYAN NYO NG CARTESIAN PLANE
Questions:
Create a Cartesian Plane and plot the points of the following coordinates and label them accordingly. 1. (-2 , 5) 2. ( 6 ,-3) 3. ( 4 , 2) 4. (-4 ,-2) 5. (-3 ,-4)
System of Linear Equations in 2 variables
Review:
- Addition and Subtraction of Real Numbers
Introduction:
A system of linear equations in two variables refers to at least two linear equations with two unknowns. The objective is to find the ordered pair, which when applied to the two equations would make them both true.
Examples:
x– y = 2 (Equation 1) x + 2y = 8 (Equation 2)
If x = 4 and y = 2:
4 – 2 = 2 Substitute x and y with their corresponding values.
4 + 2(2) = 8
The substitutes make both the equations true, therefore, ( 4 , 2 ) is the correct ordered pair.
Questions:
Identify whether the ordered pair correctly corresponds with the equations. Write true or false beside each equation. 1. x + y = 10 true x = 6 x - y