Download Equations of Parallel and Perpendicular Lines

Equations of Parallel and Perpendicular Lines
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To write the equation of a line, a point and slope are needed
Sometimes this information is not given directly
We have to problem solve to find the information we need
Remember that parallel lines have equal slopes and perpendicular lines
have slopes that are negative reciprocals to one another
Example:
Write the equation of a line parallel to 3x – 2y = 6, and which goes
through the point A(4, -2).
Solution:
3x – 2y = 6
-2y = -3x + 6
y=
– 3,
so, m =
 So the slope of the line parallel to 3x – 2y = 6 also has a slope m =
 Substituting in the given point and slope to the Point-slope equation of a
line gives us:
So,
y – y1 = m(x – x1)
y+2=
And, y =
–8
y – (-2) = (x – 4)
–6
y=
2y = 3x – 16
y+2=
-
– 8 (Slope-intercept Form)
3x – 2y – 16 = 0 (General Form)
3x – 2y = 16 (Standard Form)
Example:
Write the equation of a line perpendicular to 4x + 2y = 7, and which
goes through the point A(-2, 5).
Solution:
4x + 2y = 7 has slope
m=
=
= -2
m = -2
 So the slope of the line perpendicular to 4x + 2y = 7 has slope m =
 Substituting in the given point and slope to the Point-slope equation of a
line gives us:
So,
y – y1 = m(x – x1)
y=
And, y =
+6
y – 5 = (x – (-2))
y – 5 = (x + 2)
y–5=
+ 6 (Slope-intercept Form)
2y = x + 12
x – 2y + 12 = 0 (General Form)
x – 2y = -12 (Standard Form)
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