Parallel lines PARALLEL LINES
Linear Equations
I can find the equation of a line parallel to a
given line passing through a given point.
Essential Question: Do you use the x- or ycoordinate to find the equation parallel to x=8?
How do you know?
PARALLEL LINES ARE LINES IN THE SAME PLANE THAT
NEVER INTERSECT
 The symbol for parallel lines is
 Sketch a graph of two parallel lines.
 You can determine if two lines are parallel by comparing the slopes and y-intercepts
of the lines.
WHEN WILL LINES BE PARALLEL?
 Non-vertical and non-horizontal lines will be parallel when they have the same slope
and different y-intercepts.
 Example:
y=2x+1 is parallel to y=2x+7
 Vertical lines are parallel when they have different x-intercepts. (Remember all
vertical lines have an undefined slope)
 Example:
x=4 is parallel to x=9
 Horizontal Lines will be parallel when they have different y-intercepts. (Remember
all horizontal lines have a zero slope)
 Example:
y=-1 is parallel to y=15
STEPS TO WRITE EQUATION A LINE PARALLEL TO A NONVERTICAL, NON-HORIZONTAL LINE PASSING THROUGH A
GIVEN POINT.
EXAMPLE: FIND THE EQUATION OF A LINE PARALLEL TO Y=3X+1 THAT PAS SES THROUGH THE POINT (2, 1)
1.
Find the slope of the given line. This
will be the slope of your new line.
2. Determine x and y from the given
point.
3.
4.
Substitute m, x and y into the
equation y=mx+b and solve for b.
Substitute your m and b into
y=mx+b
m=3.
x=2 and y=1
1=3(2)+b
1=6+b
-5=b
y=3x-5
STEPS TO WRITE THE EQUATION OF THE LINE
PARALLEL TO A VERTICAL LINE
EXAMPLE: FIND THE EQUATION OF A LINE PARALLEL TO X=5 THAT PASSES THROUGH (2, 1)
1.
Determine the x-coordinate of the
point
2.
Write the equation of the line as
x=_____
The x-coordinate is 2
x=2 is the equation of the line
STEPS TO FIND THE EQUATION OF A LINE PARALLEL TO
A HORIZONTAL LINE PASSING THROUGH A GIVEN
POINT
EXAMPLE: FIND THE EQUATION OF THE LINE PARALLEL TO Y=3 THAT PASS ES THROUGH THE POINT (9, 0)
1.
Find the y-coordinate of the given
point.
2.
Write the equation of the line as
y=_______
The y-coordinate is 0
The equation of the line is y=0