Intersection of Graphed Equations

My Definition

Key Characteristics

The following are true of the intersection of graphed equations:

- It can be a point (
*x*,*y*) that occurs on both graphed equations. - It represents a solution(s) that satisfies both equations.
- Not all pairs of graphed equations will have an intersection.
- Coinciding lines will have an infinite number of intersections.

Example

Consider the two equations *y* = 4*x* and *y* = 2*x* + 6. The intersection of these two graphed equations represents a solution to both equations.

Follow the instructions below to further study examples of the intersection of graphed equations.

- 1. Go to the Intersection of Graphed Equations Activity.
- 2. Use this screen capture for instructions to obtain the ordered pairs.
- 3. Enter 4
*x*into the left side of the balance and 2*x*+ 6 into the right side of the balance. Move the slider for*x*to zero. What do you notice? - 4. Move the slider for
*x*to -3. What do you notice? - 5. Move the slider for
*x*to 3. What do you notice? - 6. (3, 12) represents the intersection of the graphed equations
*y*= 4*x*and*y*= 2*x*+ 6. - 7. Repeat steps 1 to 6 using these two equations:
*y*= 2*x*;*y*=*x*- 4 - 8. Repeat steps 1 to 6 using these two equations:
*y*= -2*x*- 1;*y*=*x*+ 5 - 9. Repeat steps 1 to 6 using these two equations:
*y*= 2*x*+ 4;*y*=13x - 3

Non-example

The ordered pair (2,4) is one solution to the equation *y* = 2*x*. The ordered pairs (3, 6), (4.5, 9), and (5.2, 10.4) are also solutions to the equation *y* = 2*x*.

*y* = 2*x*

4 = 2(2)

4 = 4

TEKS: 5(8)(A), 8(9)(A)