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Algebra I Recipe: Graphing Linear Equations with Two Variables
A. How to Determine if a Given Point is a Solution to a Given Equation
  1. Substitute the x and y values from the ordered pair into the equation for x and y.
  2. Perform all operations until a true or false statement can be determined.
    • If a true statement is the result, then the point is a solution to the equation.
    • If a false statement is the result, then the point is NOT a solution to the equation.
  3. If an ordered pair is a solution to an equation, then the point would lie on the graph of the equation.
Is (-1, -7) a solution to 6x - 2y = 8?
Is (-1, -1) a solution to –2x - 9y = 7?
Is (-2, 8) a solution to 2y - 4x = 8?
Is (2, -1) a solution to 6y - 3x = -9?
B. Graphing a Linear Equation using the “Box Method” (or table of values)
  1. Draw a box with a vertical x column, a vertical equation column, a vertical y column, and a vertical (x,y) column.
  2. Choose –2, -1, 0, 1, 2 for x into the box.
  3. Substitute these x-values into the equation one at a time.
  4. Solve the equation for y for each different x-value and put the y-values you obtain into the box.
  5. Five ordered pairs or points have been found.
  6. Graph the five points.
  7. Connect the points with a straight line with arrows on each end.
  8. Label the line with its equation.
y = -2x + 5
y = -(3 - x)
y = -¾x + 1
x - 2y = 6
x = 9
y = -1

G Redden

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