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Parallel, Perpendicular, or Neither?

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This document discusses identifying whether lines are parallel, perpendicular, or neither based on their slope and y-intercept characteristics. It provides examples of lines that are parallel because they have the same slope but different y-intercepts, lines that are neither because they have different slopes that are not opposite reciprocals, and rewriting line equations in slope-intercept form to identify lines that are perpendicular because they have opposite reciprocal slopes.

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PARALLEL, PERPENDICULAR, OR NEITHER Practice Problems
REMEMBER THE CHARACTERISTICS: Characteristic Parallel Lines Perpendicular Lines Slope Same or Equal Opposite Reciprocals Y-Intercepts Different Same or Different
PARALLEL, PERPENDICULAR, OR NEITHER? = 3 + 2 and = 3 4
THESE LINES ARE PARALLEL BECAUSE THEY HAVE THE SAME SLOPE, BUT DIFFERENT Y-INTERCEPTS. The first line has a slope of 3 and a y-intercept of 2. The second line has a slope of 3 and a y-intercept of -4.
PARALLEL, PERPENDICULAR, OR NEITHER? = 3 2 and = 3 + 4
THESE LINES ARE NEITHER BECAUSE THEY HAVE DIFFERENT SLOPES, BUT THOSE SLOPES ARENT OPPOSITE RECIPROCALS. The first line has a slope of 3 and a y-intercept of -2. The second line has a slope of -3 and a y-intercept of 4.
PARALLEL, PERPENDICULAR, OR NEITHER? + 3 = 12 and 6 2 = 12
IT WOULD BE EASIER TO DO THIS PROBLEM IF THE EQUATIONS WERE IN SLOPE-INTERCEPT FORM, SO BEGIN BY REWRITING THEM. + 3 = 12 Subtract x on each side: 3 = + 12 Divide each term by 3: = 1 3 + 4 This line has a slope of 1 3 and a y- intercept of 4. 6 2 = 12 Subtract 6x on each side: 2 = 6 + 12 Divide each term by -2: = 3 6 This line has a slope of 3 and a y- intercept of -6.
THESE LINES ARE PERPENDICULAR BECAUSE THEY HAVE OPPOSITE RECIPROCAL SLOPES. The first line has a slope of -1/3. The second line has a slope of 3/1.

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Parallel, Perpendicular, or Neither?

  • 2. REMEMBER THE CHARACTERISTICS: Characteristic Parallel Lines Perpendicular Lines Slope Same or Equal Opposite Reciprocals Y-Intercepts Different Same or Different
  • 4. THESE LINES ARE PARALLEL BECAUSE THEY HAVE THE SAME SLOPE, BUT DIFFERENT Y-INTERCEPTS. The first line has a slope of 3 and a y-intercept of 2. The second line has a slope of 3 and a y-intercept of -4.
  • 6. THESE LINES ARE NEITHER BECAUSE THEY HAVE DIFFERENT SLOPES, BUT THOSE SLOPES ARENT OPPOSITE RECIPROCALS. The first line has a slope of 3 and a y-intercept of -2. The second line has a slope of -3 and a y-intercept of 4.
  • 7. PARALLEL, PERPENDICULAR, OR NEITHER? + 3 = 12 and 6 2 = 12
  • 8. IT WOULD BE EASIER TO DO THIS PROBLEM IF THE EQUATIONS WERE IN SLOPE-INTERCEPT FORM, SO BEGIN BY REWRITING THEM. + 3 = 12 Subtract x on each side: 3 = + 12 Divide each term by 3: = 1 3 + 4 This line has a slope of 1 3 and a y- intercept of 4. 6 2 = 12 Subtract 6x on each side: 2 = 6 + 12 Divide each term by -2: = 3 6 This line has a slope of 3 and a y- intercept of -6.
  • 9. THESE LINES ARE PERPENDICULAR BECAUSE THEY HAVE OPPOSITE RECIPROCAL SLOPES. The first line has a slope of -1/3. The second line has a slope of 3/1.