Luttrell 2012
89
Name: ______________________
Date: _____
6e –Parallel Lines
A set of lines may be either parallel or not. No fuzzy logic here! Parallel lines never intersect.
Looking at a graph isn’t a good indicator because the lines could be getting closer little by little.
So determine if the lines are parallel by comparing the slopes.
If the slopes are equal, then the
lines are parallel.
If the slopes and intercepts are equal, then the lines are the same!
E
x
ample A: Is 2
x
-
y
= 5 parallel to 4
x
- 2
y
= 1?
Solution: Writing the equations into slope-intercept form:
y
= 2
x
- 5 and
y
= 2
x
- ½ , it is
obvious both have slopes of 2.
Y
es, the
y
are parallel.
E
x
ample B: Find the linear equation parallel to 3
x
-
y
= 5 that is passes through (0,2).
Solution: First find the slope, which is 3. Then using point-slope form, fill in the point and
the slope:
y
- 2 = 3(
x
-0). Simplif
y
the equation to slope-intercept form:
y
= 3
x
+ 2.
This equation can also be written as -3
x
+
y
= 2 or 3
x
-
y
= -2.
E
x
ample C: Find the linear equation parallel to 2
x
- 3
y
= 1 that passes through (1,2).
Solution: Slope of the line is ⅔, plug into point-slope form:
y
-
2 = ⅔(
x
-1). Simplif
y
into
standard form b
y
getting rid of fraction - multipl
y
b
y
denominator of slope:
3
y
- 6 = 2(
x
-1). Bring
x
and
y
together on one side of equation: -2
x
+ 3
y
= 4.
This equation can also be written as 2
x
- 3
y
= - 4.
There is a pattern in the examples that make finding parallel lines easier. Be on the look-out!
1. Determine which of the following lines are parallel. Show
y
our work.
A. 3
x
- 2
y
= 5
B. 6
x
+ 9
y
= 1 C. 6
x
- 4
y
= 4 D. 9
x
+ 6
y
= 1
2. Write the linear equation that is parallel to
x
- 3
y
= 1 and passes through the point (4, 2).
3. Write the linear equation that is parallel to 5
x
- 3
y
= 1 and passes through the point (- 4, 2).
4. Write the linear equation in standard form that is parallel to 4
x
+ 9
y
= 3 and intersects (4,-2).
