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Finding Line Intersections in Linear Equations

In this guide, we will explore how to determine where graphs of linear equations intersect. We will cover concepts such as parallel lines, graphing equations, and finding solutions to systems of equations. For example, we'll analyze systems like (y = x + 3) and (y = 3x - 12) to find their intersection points, as well as assess other pairs like (y = -2x + 4) and (y = x - 2). You'll gain insights into identifying intercepts and understanding when lines are parallel or coincident.

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Finding Line Intersections in Linear Equations

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  1. Where do these graphs intersect

  2. Are These Parallel? 1. y = x + 3 y = 3x - 12 3. y – x = 1 y = -x - 1 2. y = 1/3x + 3 y = -1/3x + 3 4. 2y = 4x + 3 4y = 8x - 12

  3. Lets try one: Find the solution to the following system: m=-2 b=4 y = -2x+4 y = x -2 m=1 b=-2 • Step 1:Graph both equations • Step 2: Find • Where the lines intersect? THE SOLUTION: (2,0)

  4. y = 2x – 1 y = –x + 5 You try: Where do the lines intersect? • Graph both equations • Where do they intersect?

  5. Try again: Find the solution to the system y = -2x-1 y = -2x+4 • Graph both equations • Where do they intersect?

  6. Find the Solution

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