Transcript Section 1-2 - MrsBarnesTrig

Section 1-2
Slopes of Lines
Slope

The slope of a nonvertical line is a number
measuring the steepness of the line relative
to the x-axis; it is the ratio of the rise to the
run.
rise y 2  y1
m

run x2  x1
Important facts about the
slope of a line:
1.
a. Horizontal lines have a slope of zero
b. Vertical lines have no slope
** Having no slope is quite different from having
zero slope – see diagram on p. 8
Important facts about the
slope of a line:
2. Lines with positive slopes rise to the right –
the greater the slope the more steeply the
line rises – see diagram p. 8
Important facts about the
slope of a line:
3. Lines with negative slopes fall to the right –
the greater the absolute value of the slope
the more steeply the line falls – see diagram
p. 8
Slope of a line
The slope of y = mx + k is m. Since m is a
constant value, the slope of a line is constant.
** Since slope is constant, any two points on
the line will give the same value for the slope.
 The numbers m and k in y = mx + k provide
us with a mental picture of the line, m is the
slope and k is the y-intercept.

Slope-intercept form
y = mx + k is the slope-intercept form.
 We are used to seeing y = mx + b – in this
book they use k instead of b.
 Feel free to use b or k
Slopes of Parallel Lines

Two nonvertical lines are parallel if and only if
they have the same slope.
Activity page 10
a. 1 and  2 are complementary
 1 and  3 are congruent
b.  2 and  3 are complementary
c.
the red and blue segments are
perpendicular
rise a

d. the slope of the red segment =
run
the slope of the blue segment
b
rise
b
b



= run  a
a
Slopes of Perpendicular Lines

Two lines are perpendicular if and only if their
slopes are negative reciprocals of each other.
That is, if the slopes are and , then
1
m1  
or m1  m2  1
m2
Example
Find the slope of the line joining the given
points: (2, -6) and (8, -3)
Example
Find the slope and y-intercept of the line whose
equation is given:
a. y = 3x + 4
b.
4x + 3y = 9
Example
A line l has equation x + 2y = 5. What is the
slope of a line parallel to line l? Perpendicular
to line l?
Example
Find the value of k if the line joining (2, K) and
(4, 5) are the line y = 3x + 1 are parallel?
Perpendicular?