key term - 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

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.