Slope

1
Slope
The slope of a line is the change in y values
divided by the change in x values for any two
points on the line.
2
Slope
y2
(x2 , y2)
(x1 , y1)
y1
x1
x2
3
Slope
RUN
y2
(x2 , y2)
RISE
(x1 , y1)
y1
x1
x2
4
Possibilities for a Lines Slope
5
Examples

• Find the slope of the line through (6,8) and (-2,
  4)
• Answer -3/2
• Find the slope of the line through (2,5) and (-1,
  -5)
• Answer 0
• 3. Find the slope of the line through (2,5) and
  (-1, -5)
• Answer Undefined Slope

6
Examples
2x 3y 6 0 -3y 6 -2x -3y -2x - 6 3y
2x 6 y (2/3) x 2
7
Examples
2x 3y 6 0 -3y 6 -2x -3y -2x - 6 3y
2x 6 y (2/3) x 2
8
SlopeIntercept of a Line
A linear equation is written in the slope
-intercept form if it is in the form ymx b,
where m is the slope (0,b) is the y-intercept.
If an equation of a line is in the slope
intercept form then the slope is the coefficient
of x.
If an equation of a line is in the slope
intercept form then the y-intercept is the
constant term in the equation.
The intercept in the slope-intercept form of a
line is the y-intercept.
9
Examples
Find the slope of the line 2x 4y 5. Answer
-1/2 Find the slope of the line y -8 Answer
0 Find the slope of the line y 2x -7
Answer -2
10
Parallel Lines
Line 1
Line 2
Two non-vertical lines with the same slope are
parallel.
11
Perpendicular Lines
Line 1
Line 2
Two lines are perpendicular is the product of
their slopes equals -1.
12
Examples
Decide whether the pair of lines are parallel,
perpendicular, or neither 3x y 4 and x
3y 9 Answer perpendicular What is the slope
of the line whose graph is parallel to the graph
of 2x 4y 5 Answer -1/2 Decide whether
the pair of lines are parallel, perpendicular, or
neither 5x 3y -2 and 3x- 5y -8 Answer
Neither