Parallel and Perpendicular Math Example 1

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Example 1

easy
Find the equation of the line through (3,−1)(3, -1) that is parallel to y=2x+5y = 2x + 5.

Solution

  1. 1
    Parallel lines have equal slopes. The slope of y=2x+5y = 2x + 5 is m=2m = 2, so the new line also has m=2m = 2.
  2. 2
    Use point-slope form: y−(−1)=2(x−3)y - (-1) = 2(x - 3).
  3. 3
    Simplify: y+1=2x−6y + 1 = 2x - 6, so y=2x−7y = 2x - 7.

Answer

y=2x−7y = 2x - 7
Parallel lines never intersect because they have identical slopes. To find a parallel line through a specific point, keep the slope the same and use point-slope form to determine the new yy-intercept.

About Parallel and Perpendicular

Parallel lines never intersect and have matching direction; perpendicular lines intersect at right angles.

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More Parallel and Perpendicular Examples

Example 2 medium

Find the equation of the line through [formula] that is perpendicular to [formula].

Example 3 easy

Are the lines [formula] and [formula] parallel, perpendicular, or neither?

Example 4 medium

Line [formula] passes through [formula] and [formula]. Find the equation of the line perpendicular t

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