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How to Graph a Solution Using the Slope-Intercept Method of Solving a System of Equations

Linear equations have a general form of ax + by = c, where "a" and "b" are numerical coefficients, "x" and "y" are variables and "c" is a numerical constant. Linear equations graph as straight lines, but graphing requires the equation be converted to slope-intercept form, which states y = mx + b, where "m" is the slope and "b" is the y-intercept. A system of linear equations is a set of two or more multivariable equations that can be solved at the same time because they're correlated.

Instructions

- 1
  Solve a system of equations containing 2x - 3y = -2 and 4x + y = 24. Convert the first equation to slope intercept form by subtracting 2x from both sides -- -3y = -2x + -2 -- then divide by -3 -- y = (2/3)x + (2/3). Convert the second equation by subtracting 4x from both sides -- y = -4x + 24.
- 2
  Create a T-chart with three columns to find more points for the line. Head the first column as "x," the second as the equation y = (2/3)x + (2/3) and the third as the equation y = -4x + 24. Select test values of "x" that make the first equation turn out a whole number answer.
- 3
  Test the equations using "x" values of -4, -1, 2, 3 and 5. Solve the first equation using -4 -- y = (2/3)(-4) + (2/3) = -8/3 + 2/3 = -6/3 = -2. Solve the second equation using -4 -- y = -4(-4) + 24 = 16 + 24 = 40.
- 4
  Solve both equations using -1 -- y = (2/3)(-1) + (2/3) = 0; y = -4(-1) + 24 = 28. Solve both equations using 2 -- y = (2/3)(2) + (2/3) = (6/3) = 2; y = -4(2) + 24 = 16. Solve both equations using 5 -- y = (2/3)(5) + (2/3) = (12/3) = 4; y = -4(5) + 24 = 4. Note that the point (5, 4) appears in both lines and must be a solution and that the other answers differ so they aren't the same line.
- 5
  Graph the points found for both lines, including the y-intercepts provided by their slope intercept forms. Draw a darker dot at the point of intersection and clearly label it on the graph.

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