Home >> Science & Nature >> Science

Step-by-Step Directions for Graphing Linear Equations

Linear equations graph as a straight line based on the slope intercept form, which states y = mx + b where "m" is the slope and "b" is the y-intercept, or point where the line crosses the y-axis. The slope creates the angle of the line and is defined by the distance between a point and the next point on the line. Slope is referred to as being "rise over run" because it causes a movement on the y-axis, then on the x-axis. For example, a slope of 2 would cause a point to shift 2 spaces up (y-axis) followed by 1 space right (x-axis).

Instructions

- 1
  Convert the given linear equation to slope intercept form and identify the slope and y-intercept: for example, with the equation 2y - 4x = 8, first add 4x to both sides for 2y = 4x + 8. Divide both sides by 2: y = 2x + 4, where the slope is 2, or 2/1, and the y-intercept is 4, or point (0, 4).
- 2
  Apply the slope to the y-intercept point to find new points for the line, remembering that the slope represents movement on the y-axis, then the x-axis: (0 + 1, 4 + 2) = (1, 6). Apply the slope to the new point: (1 + 1, 6 + 2) = (2, 8). Subtract the slope from the y-intercept to find a point behind it on the line: (0 - 1, 4 - 2) = (-1, 2). Subtract the slope from the new point: (-1 - 1, 2 - 2) = (-2, 0), which is the x-intercept.
- 3
  Graph dots for the found points; then use a ruler to draw a straight line of connection. Draw arrows on each end of the line to represent continuation.

Science