VERTICAL AND HORIZONTAL LINESFinding the equations of

HOW TO KNOW WHICH IS WHICH…

A vertical line will be written as x = #. Since the

line will have slope that is undefined, the line

will ONLY intersect the x axis.

x = 3 x = -1 x = 6

AND THE OTHER….

A horizontal line will be written as y = #. This

type of line has a zero slope, so it will only

intersect the y axis.

FINDING THE EQUATION

Find the equation of horizontal line that goes

through the point (8, 4)

Since a horizontal line is ‘flat’ line, the only way to draw a line with a zero slope through that point is draw a line through the y axis at 4.

So the line is y = 4

FINDING THE EQUATION, CON’T

Find the equation of vertical line that goes through the point (-2, 7)

A vertical line has an undefined slope. The only way

to draw a vertical line through that point is draw a

line through the x axis at -2.

So the line is x = -2

PARALLEL AND PERPENDICULAR LINES

If you have horizontal line, you know the slope is zero, which can be

written as 0/1.

A parallel line would also have a slope of 0….another horizontal line.

A perpendicular line would have a slope that is the negative reciprocal

of that…. -1/0

WHAATTT!?!?!?!?!

That is UNDEFINED which means a line that is perpendicular to a horizontal line must be vertical .

EXAMPLE 1

Find the equation of line parallel to y = 6 through the

point (4, 2).

Parallel means “same slope”… and this line has a slope of zero.

That means our parallel line must also be ‘flat’.

Y = 2

EXAMPLE 2

Find the equation of line parallel to y = 3 through the

point (-2, 12).

Parallel means “same slope”… and this line has a slope of zero.

That means our parallel line must also be ‘flat’.

Y = 12

Seeing a pattern???

EXAMPLE 3

Find the equation of line parallel to y = -9 through the point (13, -5).

Parallel means “same slope”… and this line has a slope of zero.

That means our parallel line must also be ‘flat’.

Y = -5

When the line is parallel, keep the same variable and set it equal to that coordinate value. Soooooo….

EXAMPLE 4

Find the equation of line parallel to x = -9 through the

point (13, -5).

Parallel means “same slope”… and this line has a slope that is UNDEFINED.

That means our parallel line must also be vertical.

x = 13

Now for perpendicular….

EXAMPLE 5

Find the equation of line perpendicular to x = 3 through the point (5, 7).

Perpendicular means the slope will be the negative reciprocal. Our original line is vertical, so the perpendicular slope will be zero…

making the line horizontal

So, we have a line that is horizontal (y = ) through the given point

y = 7

hhmmmmm….

EXAMPLE 6

Find the equation of line perpendicular to x = 8 through the point (9 -1).

Perpendicular means the slope will be the negative reciprocal. Our original line is vertical, so the perpendicular slope will be zero…

making the line horizontal

So, we have a line that is horizontal (y = ) through the given point

y = -1

See it yet???

THE ‘RULE’

Parallel: keep the same variable and set it equal to the value in the point.

Perpendicular: that the other variable and use the value of the other variable in the point.