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 y-coordinate 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 NON-VERTICAL, NON-HORIZONTAL LINE

PASSING THROUGH A GIVEN POINT.EXAMPLE: FIND THE EQUATION OF A LINE PARALLEL TO Y=3X+1 THAT PASSES 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. Substitute m, x and y into the equation y=mx+b and solve for b.

4. 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 LINEEXAMPLE: 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 POINTEXAMPLE: F IND THE EQUATION OF THE L INE PARALLEL TO Y=3 THAT PASSES 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