Daily Homework Quiz

Graph each line.

- x32y= 3–1.

y =2x + 62.

ANSWER

ANSWER

Daily Homework Quiz

2.4 Part 2Sept 14, 2012

Graph the lines y = -4x -3 and y = -4x +2

What do these 2 equations have in

common?

They are parallel ( ll )

What do you notice about the

lines?

Their slopes (m) are the same.

In a coordinate plane, 2 lines are parallel if and only if

they have the same slope.

Slopes of Parallel Lines

Testing if Lines are ParallelAre the lines y = ½x – 5 and y = -½ x +2 parallel?

Since the slopes are different the lines are not parallel.

Since the equations are both in standard form, rewrite both of them in y = mx + b form to find their slope and compare.

Are the lines 6x – 3y = 5 and 4x + 2y = 4 parallel?

Find the opposite reciprocal of

21- .)1 2

74 .)2 4

7-

Graph the lines y= x +3 and y= -x+3What do these 2

equations have in common?

They are perpendicular ( )

What do you notice about the

lines?

Their slopes (m) are the opposite reciprocal

In a coordinate plane, 2 lines are perpendicular if and only if their slopes are opposite reciprocal

of each other (or their product is –1)

Slopes of Perpendicular Lines

Testing if Lines Are Perpendicular

1Are the lines 2 5 and 4 perpendicular?2

x y y x

Find the slope of 2 5 22 5

x y my x

1 1Find the slope of 4 2 2

y x m

Since the slopes are negative reciprocals of each other the lines are perpendicular. 12 1

2

Extra PracticeTell whether the lines are parallel, perpendicular, or neither.

20102 and 15 .)4

431and 83 3.)

1236 and42 2.)

57 and 17 .)1

yxyx

x y x y

y x - y x

x-yxy Parallel

Perpendicular

Neither

Perpendicular

Graphing x = #Ex. Graph x = -3The x coordinate is -3 no matter what the value of y is. x y

-3 0

-3 1

-3 2

-3 3

••••

Choose any value of y

So, the graph of x = # is always a VERTICAL LINE

Ex. Graph x = 4

The graph of x = 4 is VERTICAL LINE at 4.

Graphing y = #Ex. Graph y = 2The y coordinate is 2 no matter what the value of x is. x y

0 2

1 2

2 2

3 2••••

Choose any value of x

So, the graph of y = # is always a HORIZONTAL LINE

Ex. Graph y = -4

The graph of y = -4 is HORIZONTAL LINE at -4.

Homework2.4 p.91 #32-43,

50-55