Graph in two variables

Definition

A graph in two variables represents the set of all points $(x, y)$ that satisfy a given equation involving $x$ and $y$. These points are plotted on a rectangular coordinate system, resulting in a visual representation of the relationship between the variables.

5 Must Know Facts For Your Next Test

1. A graph in two variables is drawn on the Cartesian plane using an x-axis and y-axis.
2. The solution to an equation with two variables is represented by points on the graph where both variable values satisfy the equation.
3. A linear equation in two variables forms a straight line when graphed.
4. The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
5. Intersections of graphs can reveal solutions to systems of equations.

Review Questions

• What does each point $(x, y)$ on a graph represent?
• How do you determine if a point lies on the graph of an equation?
• What is the significance of the slope and y-intercept in a linear graph?

Related terms

Cartesian Plane: A plane divided by two perpendicular axes: the x-axis (horizontal) and y-axis (vertical), used for plotting points.

Slope: The measure of steepness or incline of a line, calculated as rise over run ($m = \frac{\Delta y}{\Delta x}$).

Y-Intercept: The point where a line crosses the y-axis, represented by 'b' in the slope-intercept form $y = mx + b$.