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How Do You Graph a Linear Equation by Making a Table?

Graph y = 2x - 2.

Summary

  1. Draw coordinate axes to graph y=2x-2
  2. Make a table to find ordered pairs to plot
  3. We've picked -1, 0, and 1 to plug into the equation, which we can then solve for y
  4. We can simplify the middle column to find y
  5. When x is -1, y is -4
  6. When x is 0, y is -2
  7. When x is 1, y is 0
  8. Plot the points we just found!
  9. Connect the points we plotted to graph the line y=2x-2

Notes

    1. The x-axis is horizontal, and the y-axis is vertical
    1. The table will help us find the points we need to plot before we can graph
    1. The left-most column is for the x-coordinates
    1. The second column is for the right hand side of the equation, 2x-2
    1. The right-most column is for the y-coordinates
    1. We can pick any x-coordinates to plug into the right hand side, but it will be helpful to pick a positive one, a negative one, and 0
    1. This will help us get a better idea of what the graph does as it crosses the y-axis
    2. Sometimes, equations will do funky things when crossing the y-axis
    1. We want to pick number close to the origin because that is the only area we have available to graph on in the diagram!
    1. We are plugging x-coordinates in for 'x' in 2x-2
    2. The x-coordinates we are using are -1, 0, and 1
    1. We are plugging our values for 'x' that we chose into the right hand side of the equation
    2. Our values for x were -1, 0, and 1
    1. Remember, the right hand side is set equal to y in our equation
    2. So our middle column, which is the right hand side, will tell us what y's we have
    3. We can simplify the middle column by following the order of operations
    1. We are simplifying the middle column to find y
    2. According to the order of operations, we have to multiply first and then subtract!
    1. This gives us three ordered pairs, (-1,-4), (0,-2), and (1,0)
    1. We found (-1,-4), (0,-2), and (1,0) using the table
    1. When x is -1, y = 2(-1)-2 = -4
    1. We move left because the x-coordinate is negative
    1. We move down because the y-coordinate is negative
    1. We've just plotted the point (-1,-4)
    1. If the x-coordinate was positive we would move right, but if it was negative we would move left
    1. We move down because the y-coordinate is negative
    1. We move right because the x-coordinate is positive
    1. If the y-coordinate was positive we would move up, but if it was negative we would move down