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How to Do Linear-Equation Graphing

Linear equations contain variables, or letter representations for unknown quantities, and constants (numbers). The graph of a linear equation forms a straight line defined by its slope. The slope is the distance between a point, (x1, y1), and the point next to it, (x2, y2). The slope is defined as (y2 - y1) / (x2 - x1). The slope and the y-intercept, or point at which the line crosses the y-axis, are integral parts of the slope intercept form. Slope intercept form states y = mx + b, where "m" is the slope and "b" is the y-intercept.

Instructions

- 1
  Convert a linear equation to slope intercept form for graphing. Identify the slope and y-intercept and apply the slope to the y-intercept point to find additional points for the line.
- 2
  Graph the line (1/2)y - 3x = 2. Convert to slope intercept form. Add 3x to both sides (1/2)y = 3x + 2. Multiply both sides by 2: y = 6x + 4. Note that the slope is 6, or 6/1, and the y-intercept is 4, or point (0, 4).
- 3
  Apply the slope to the y-intercept, remembering that slope equals rise over run, or movement on the y-axis followed by movements on the x-axis: (0 + 1, 4 + 6) = (1, 10). Apply the slope to the new point (1 + 1, 10 + 6) = (2, 16). Subtract the slope from the y-intercept to find two points behind the intercept on the line: (0 - 1, 4 - 6) = (-1, -2). Subtract the slope (-1 -1, -2 - 6) = (-2, -8).
- 4
  Graph the points and draw the connecting straight line, placing arrows on each end of the line to represent continuation.

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