ACT Study Modules Topic: Finding slope from parallel and perpendicular lines
Khan Academy Link: https://www.khanacademy.org/math/geometry-home/analytic-geometry- topic/parallel-perpendicular-lines-coordinate-plane/v/classify-lines
To determine the slope of parallel lines from an equation:
Step one: arrange the equation in the form, = + Step two: determine the slope ( value) Step three: compare the slopes π¦π¦ ππππ ππ Step four: compare the β β valuesππ
If the b values are differentππ and the slope is the same, then the lines are parallel.
Example: 3 + = 9 5 = 3 Add 3 to both sides add 5 to both sides β π₯π₯ of π¦π¦the equationβ ofπ¦π¦ theβ equationπ₯π₯ π₯π₯= 3 9 = 3 + 5
In the functions, π¦π¦= 3 π₯π₯ β9 & = 3 + 5 the slope is 3, and theπ¦π¦ valuesπ₯π₯ are different, making the lines parallel. π¦π¦ π₯π₯ β π¦π¦ π₯π₯ ππ To determine the slope of perpendicular lines from an equation:
Step one: arrange the equation in the form = + Step two: determine the slope ( value) Step three: compare the slopes π¦π¦ ππππ ππ ππ If the slopes are negative reciprocals, the lines are perpendicular.
Example: 5 = 4 + 8 = 1/5 Add 5 to both sides Subtract 8 from both sides π¦π¦ β ofπ₯π₯ the βequation π¦π¦of the equationβ π₯π₯ π₯π₯= 5 4 = 3 + 5
π¦π¦ π₯π₯ β π¦π¦ π₯π₯ Slopes are 5 and -1/5, the slopes are negative reciprocals, making the lines perpendicular.
Example: In the standard ( , ) coordinate plane which of the lines are perpendicular to the line = 2 + 2 that passes through the point (0,3) π₯π₯ π¦π¦ Stepπ¦π¦ one:β determineπ₯π₯ the slope of the perpendicular line:. The slope of the original line is 2 the negative reciprocal of 2 is 1 β Step two: = + β 2 Step three: to determine1 , substitute the and - values of the point, (0,3) π¦π¦ 2 π₯π₯ ππ 3 = (0) + ππ π₯π₯ π¦π¦ 3 = 1 2 ππ Step four: write the equation, = + 3 ππ 1 π¦π¦ 2 π₯π₯ Practice:
Line Equation of a parallel line Equation of a perpendicular line
= 2 5
π¦π¦ π₯π₯ β
2 3 = 12
π₯π₯ β π¦π¦
3 = 1 4
π¦π¦ β π₯π₯ β
5 + 2 = 15
π₯π₯ π¦π¦