Graph in two variables

Definition

A graph in two variables is a visual representation of all the possible solutions to an equation involving two variables, typically plotted on a rectangular coordinate system. The horizontal axis represents one variable, while the vertical axis represents the other.

5 Must Know Facts For Your Next Test

1. The point where the graph intersects the x-axis is called the x-intercept, and where it intersects the y-axis is called the y-intercept.
2. A linear equation in two variables forms a straight line when graphed.
3. The slope-intercept form of a linear equation is given by $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
4. The solution to a system of equations in two variables can be found graphically by identifying points where their graphs intersect.
5. Quadratic equations in two variables form parabolas when graphed.

Review Questions

• What does the slope represent in a linear graph?
• How do you determine the x-intercept and y-intercept from an equation?
• What shape does a quadratic equation form when graphed?

Related terms

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

Intercept: Points where a graph crosses the axes. The x-intercept occurs where $y=0$ and the y-intercept occurs where $x=0$.

Quadratic Equation: An equation of the form $ax^2 + bx + c = 0$, which graphs as a parabola on a coordinate plane.