Coordinate Planes in Math

Study Notes

A coordinate plane is a two-dimensional grid used to graph and visualize mathematical relationships.
It consists of two perpendicular lines, the x-axis and the y-axis, which intersect at a point called the origin (0, 0).
The x-axis is the horizontal line, and the y-axis is the vertical line.
Each point on the coordinate plane is represented by an ordered pair of coordinates (x, y), where x is the horizontal distance from the origin and y is the vertical distance from the origin.

The coordinate plane is divided into four quadrants:
1. Quadrant I: x > 0, y > 0 (upper right)
2. Quadrant II: x < 0, y > 0 (upper left)
3. Quadrant III: x < 0, y < 0 (lower left)
4. Quadrant IV: x > 0, y < 0 (lower right)

A linear equation is an equation in which the highest power of the variable(s) is 1.
The general form of a linear equation is: Ax + By = C, where A, B, and C are constants.
Examples:
- 2x + 3y = 5
- x - 2y = -3

To graph a linear equation, find the x-intercept and y-intercept by setting x = 0 and y = 0, respectively.
Plot the points on the coordinate plane and draw a straight line through them.
The slope of the line (m) can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

A non-linear equation is an equation in which the highest power of the variable(s) is greater than 1.
Examples:
- x^2 + 4y = 7
- y = x^2 - 3x + 2
Non-linear equations can be graphed using various methods, such as:
- Plotting points and drawing a curve
- Using algebraic methods to find the x-intercepts and y-intercepts
- Using graphing software or calculators

A coordinate plane is a 2D grid used to graph and visualize mathematical relationships, consisting of two perpendicular lines, the x-axis and the y-axis, which intersect at the origin (0, 0).
The x-axis is the horizontal line, and the y-axis is the vertical line.
Each point on the coordinate plane is represented by an ordered pair of coordinates (x, y), where x is the horizontal distance from the origin and y is the vertical distance from the origin.

A linear equation is an equation in which the highest power of the variable(s) is 1.
The general form of a linear equation is: Ax + By = C, where A, B, and C are constants.
Examples of linear equations include 2x + 3y = 5 and x - 2y = -3.

To graph a linear equation, find the x-intercept and y-intercept by setting x = 0 and y = 0, respectively.
Plot the points on the coordinate plane and draw a straight line through them.
The slope of the line (m) can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

A non-linear equation is an equation in which the highest power of the variable(s) is greater than 1.
Examples of non-linear equations include x^2 + 4y = 7 and y = x^2 - 3x + 2.
Non-linear equations can be graphed using various methods, such as:
- Plotting points and drawing a curve
- Using algebraic methods to find the x-intercepts and y-intercepts
- Using graphing software or calculators