(x, y) is a coordinate pair that represents a specific point on a two-dimensional coordinate plane. The x-value corresponds to the horizontal position, while the y-value corresponds to the vertical position of the point. This coordinate pair is fundamental to graphing linear equations in two variables, as it allows for the visual representation of the relationship between the variables.
congrats on reading the definition of (x, y). now let's actually learn it.
The $(x, y)$ coordinate pair uniquely identifies the location of a point on a two-dimensional coordinate plane.
The $x$-value represents the horizontal position of the point, while the $y$-value represents the vertical position.
Plotting points with $(x, y)$ coordinates is a fundamental skill for graphing linear equations in two variables.
The slope of a linear equation can be calculated using the $(x, y)$ coordinates of two points on the line.
The $y$-intercept of a linear equation can be determined by finding the $y$-value when $x = 0$, or the $(0, y)$ coordinate.
Review Questions
Explain how the $(x, y)$ coordinate pair is used to represent and plot points on a two-dimensional coordinate plane.
The $(x, y)$ coordinate pair is used to specify the location of a point on a two-dimensional coordinate plane. The $x$-value corresponds to the horizontal position, while the $y$-value corresponds to the vertical position. By plotting the point with the given $(x, y)$ coordinates, you can visually represent the relationship between the two variables on the coordinate plane. This is an essential skill for graphing linear equations in two variables, as the $(x, y)$ coordinate pair allows you to plot the points that make up the line.
Describe how the $(x, y)$ coordinate pair is used to determine the slope of a linear equation.
The slope of a linear equation can be calculated using the $(x, y)$ coordinates of two points on the line. The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points. By substituting the $x$ and $y$ values into this formula, you can determine the slope of the line, which is a crucial characteristic for understanding the behavior and graphing of linear equations in two variables.
Analyze how the $(x, y)$ coordinate pair can be used to identify the $y$-intercept of a linear equation in slope-intercept form.
In the slope-intercept form of a linear equation, $y = mx + b$, the $y$-intercept is represented by the $b$ value. This $y$-intercept can be identified by finding the $y$-value when $x = 0$, which corresponds to the $(0, y)$ coordinate pair. By substituting $x = 0$ into the equation, you can solve for the $y$-value, which gives you the $y$-intercept of the line. Understanding how to use the $(x, y)$ coordinate pair to determine the $y$-intercept is crucial for graphing linear equations in two variables.