1. 3.6 PARALLEL LINES IN THE COORDINATE PLANE 1 m = GOAL
SLOPE OF PARALLEL LINES
y2 - y1
m =
x2 - x1
EXAMPLE 1

2. Extra Example 1
The Cog Railway covers about 3.1 miles and gains about 3600 feet of altitude. What is the average slope of the track?

3. m = m = = When you use the formula for the slope,
y2 - y1
m =
x2 - x1
m =
run change in x
rise change in y =
y2 - y1
x2 - x1
Subtraction order is the same
the numerator and denominator
must use the same subtraction order.
CORRECT
x1 - x2
y2 - y1
Subtraction order is different
INCORRECT
The order of subtraction is important. You can label either point as (x1, y1)
and the other point as (x2, y2). However, both the numerator and denominator
must use the same order.
numerator
y2 - y1
denominator
x2 - x1
EXAMPLE 2

4. Extra Example 2
Find the slope of a line that passes through the points
(–3, 0) and (4, 7).

5. Vertical lines are parallel.
POSTULATE
In the coordinate plane, nonvertical lines are parallel if and only if they have the same slope.
Vertical lines are parallel.
EXAMPLE 3

6. Extra Example 3
Find the slope of each line.
EXAMPLE 4

7. Extra Example 4
Line p1 passes through (0, –3) and (1, –2). Line p2 passes through (5, 4) and (–4, –4). Line p3 passes through (–6, –1) and (3, 7). Find the slope of each line. Which lines are parallel?

8. Checkpoint
Line k1 passes through (8, –1) and (–5, –9). Line k2 passes through (–6, –5) and (7, 3). Line k3 passes through (10, –4) and (–3, –4). Find the slope of each line. Which lines are parallel?

9. We will write equations in slope-intercept form:
3.6
PARALLEL LINES IN THE COORDINATE PLANE
GOAL 2
WRITING EQUATIONS OF PARALLEL LINES
We will write equations in slope-intercept form:
EXAMPLE 5

10. Extra Example 5
Write an equation of the line through the point (4, 9) that has a slope of –2.

11. Checkpoint
Write an equation of the line through the point (20, 5) that has a slope of
EXAMPLE 6

12. Extra Example 6 Line k1 has the equation Line k2 is parallel to
k1 and passes through the point (–5, 0). Write an equation
of k2.

13. Checkpoint
Line m1 has the equation y = 3x – 7. Line m2 is parallel to m1 and passes through the point (–2, 1). Write an equation of m2.

14. QUESTION:
What are the six methods we have available to prove two lines are parallel?
ANSWER:
1-3: Show alternate interior angles, alternate exterior angles, or corresponding angles are congruent.
4: Show consecutive interior angles are supplementary.
5: Show that the lines are perpendicular to the same line.
6: Show that the lines are parallel to the same line.