Coordinate Plane

Definition

The coordinate plane, also known as the Cartesian coordinate system, is a two-dimensional graphical representation used to locate and visualize points, lines, and other geometric shapes. It consists of a horizontal x-axis and a vertical y-axis that intersect at a point called the origin, forming a grid-like structure that allows for the precise mapping of coordinates.

5 Must Know Facts For Your Next Test

1. The coordinate plane is used to graph and visualize linear equations, linear inequalities, functions, and systems of equations and inequalities.
2. The slope of a line can be determined by the rise (change in y-value) and run (change in x-value) between any two points on the line.
3. The equation of a line in the coordinate plane can be written in the form $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.
4. Linear inequalities in two variables can be graphed on the coordinate plane by shading the region that satisfies the inequality.
5. Functions can be graphed on the coordinate plane, and the graph of a function represents the set of all ordered pairs (x, y) that satisfy the function.

Review Questions

• Explain how the coordinate plane is used to graph linear equations in two variables.
  • The coordinate plane provides a visual representation of linear equations in two variables, where the x-axis represents the independent variable and the y-axis represents the dependent variable. To graph a linear equation, you plot points on the coordinate plane using the ordered pairs (x, y) that satisfy the equation. By connecting these points, you can create the graph of the linear equation, which will be a straight line. The slope and y-intercept of the line can be determined from the equation and used to help sketch the graph.
• Describe how the coordinate plane is used to determine the slope of a line.
  • The slope of a line on the coordinate plane is the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between any two points on the line. To find the slope, you can select two points on the line and calculate the slope using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. The slope represents the steepness of the line and is a crucial component in determining the equation of the line in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
• Explain how the coordinate plane is used to graph and solve systems of linear inequalities.
  • The coordinate plane is used to graph and solve systems of linear inequalities by plotting the boundaries of each inequality and identifying the region where all the inequalities are satisfied. To graph a linear inequality, you plot the line that represents the equality, and then shade the region that satisfies the inequality. By graphing multiple linear inequalities on the same coordinate plane, you can find the common intersection region, which represents the solution to the system of linear inequalities. This method allows you to visualize and determine the feasible solutions to the system.

Related terms

Quadrants: The coordinate plane is divided into four regions called quadrants, each identified by a Roman numeral (I, II, III, IV) based on the signs of the x and y coordinates.

Ordered Pair: A set of two numbers that represent the x and y coordinates of a point on the coordinate plane, typically written in the form (x, y).

Origin: The point where the x-axis and y-axis intersect, with coordinates (0, 0), which serves as the reference point for the coordinate plane.