1.3 Lines
1 Calculate and inter pret the slope of a Line (p. 20)
(1) Defintion
Let 
be two distinct points. If
, the slope m of
the nonvertical line L containing P and Q is defined by the formula
If 
, L is a
and the slope m of L
is .
(2) Sketch the plot of the following equations, find its slope and de termine
whether the line is
slants upward, slants downward, horizontal or vertical.
| Equations |
Sketch |
Slope |
Type |
 |
 |
|
|
 |
|
m = 2 |
Slant upward |
 |
|
|
|
 |
|
|
|
(3) Finding and Interpreting the Slope of a Line
2 Graph Lines Given a Point and the Slope (Slope is
defined) *
(1) Graph the point (x, y) on the Cartesian coordinate system
(2) Write the slope as 
(Rise is integer and
Run are positive integer )
(3) Graph another point (x + Run, y + Rise)
(4) Drawing the line through the two points
3 Find the Equation of a Line
(1) Equations of a line
|
Equation of a Vertical Line (p. 24) |
|
A vertical line is given by an equation of the form
Where a is the x-intercept. |
|
Equation of a Horizontal Line (p. 25) |
|
A horizontal line is given by an equation of the form
Where b is the y-intercept. |
|
Point-Slope Form of an Equation of a Line (p. 24) |
An equation of a nonvertical line with slope m that
contains the point  is
|
|
Slope- Intercept Form of an Equation of a Line (p. 25) |
|
An equation of a nonvertical line with slope m and
y-intercept b is
|
|
General Form (p. 27) |
| The general form of the equation of a line is
Where A, B and C are real numbers and A and B are
not both 0. |
(2) Find the Equation of a Vertical Line
(3) Find the Equation of a Horizontal Line
(4) Find the Equation of a General Line
a) Known a point and the slope, use the point-slope form
b) Known the slope and the y-intercept, use the slope-intercept form
c) Known two points, use the general form
d) Then substitute the known conditions into the relative form, and simplify the
equation
(5) Identify the Slope and y-intercept of a Line from Its Equation
Write the equation of the line as the slope-intercept form: y = m x + b
(6) Graph the line with equation in different form
a) Known point-slope form, 
, see 2
b) Known slope-intercept form, y = mx + b, graph one point (b, 0) and the follow
the steps
(2)-(4) in 2
c) Known the general form, Ax + By = C, then follow these steps
• substitute x=0 into the equation, and solve it for y, denoted as
• substitute y=0 into the equation, and solve it for x, denoted as
• graph two points 
and
• draw the line through two points
3 Parallel Lines
(1) Criterion for Parallel Lines
Two nonvertical lines are parallel if and only if their slopes are equal and
they have different
y-intercepts.
(2) Equation of two parallel lines
(3) Showing that two lines are parallel
a) Find their slopes and y-intercepts
b) Compare their slopes: they are NOT parallel with different slopes
c) Compare their y-intercepts: they are NOT parallel with the same y-intercept
(4) Finding a line that is parallel to a given line
a) Write the equation of the given line into the slope-intercept form
b) Assume the equation of the parallel line is
c) Substitute the known equation into the equation, and solve for
4 Find Equations of Perpendicular Lines
(1) Definition
When two lines intersect at a right angle (90ยบ), they are said to be
perpendicular.
(2) Criterion for Perpendicular Lines
Two nonvertical lines are perpendicular if and only if the product of their
slopes is -1.
(3) Equation of two vertical lines
(5) Finding a line that is perpendicular to a given line
a) Write the equation of the given line into the slope-intercept form
b) Assume the equation of the parallel line is
c) Substitute the known equation into the equation, and solve for
