Linear Equation in Two Variables

The following concepts are important:
  • A linear equation in two variables results in infinitely many pairs of solutions.
  • Since solutions come in pairs of values of x and y, each pair of solutions may be represented by a point on the Cartesian Plane.
  • The complete set of solutions of a linear equation in two variable on the Cartesian Plane forms a line.
  • Thus, we must understand that the graph of an equation is the visual representation of the list of solutions of an equation with two variables.
1. You can adjust the values of A, B and C using the sliders. A changes the coefficient of x, B changes the coefficient of y, and C is the constant. 2. You can move the point P along the line. Note that each ordered pair on the line satisfies the equation. 3. Note the points of the line along the x-axis and the y-axis. The point on the x-axis is called the X-INTERCEPT of the line. The point on the y-axis is called the Y-INTERCEPT of the line. 4. What happens when A = 0? What happens when B = 0? 5. What other observations can you make about the line when you adjust the values of A, B and C?