techmathi - 3.1 - lines in space day2

Bell RingerFind a line parallel to each.

1.y = 3x - 1, (-1, -4)

2.y = -2x + 12, (3, -9)

3.m = ½x - 4, (2, 5)

Perpendicular Lines- Two lines are perpendicular if their slopes are negative reciprocals- “flip the fraction and change the sign”`

Write an equation of a line perpendicular that passes through the following point:1.m = 3, (-1, 3)

2. m = ½, (2, -3)

3. m = -3, (0, 6)

You try !Find a line perpendicular that passes thru each

point.

1.m = 4, (-1, -6)

2.m = 3/2 , (8, 4)

3.m = -1, (3, -4)

Rate of Change

Rate of change = Change in yChange in x

# of days Rental Charge

1 60

2 80

3 100

4 120

5 140It costs $______ per day.

Rate of Change

Rate of change = Change in yChange in x

Miles Fee Charged

100 30

150 42

200 54

250 66

300 78It costs $______ per mile.

You try!

Day Amount Owed

1 135

2 120

3 105

4 90

5 75

After every 1 day, the price decreases by $______.

People Cost

2 7.90

3 11.85

4 15.80

5 19.75

6 23.70

For every 1 person, the price is $______.

1. 2.

The Rate of Change of a line is called its SLOPE.

Slope

rise runSlope = y2 – y1

x2 – x1

=

If you are given two sets of points,

(x1 , y1) and (x2 , y2)

you can find the slope using the formula above.

rise runSlope = y2 – y1

x2 – x1

=

Find the slope of the line through A(-2 , 1) and B(5 , 7)

Find the slope of the line through A(-1 , 3) and B(7 , 9)

Find the slope of the line through A(1 , 2) and B(7 , 4)

Find the slope of the line through A(0 , 5) and B(6 , -7)

Find the slope of the line through A(-2 , 4) and B(0 , -6)

You try!

Intersections of Lines- To see the point where two lines intersect,

set them equal and solve for x.

Example 1:y = 2x + 2y = 4x + 12

Example 2:y = 3x + 8y = -2x + 17

Example 3:y = -x - 12y = -3x + 10

You try!Example 1:y = 6x + 1y = -4x + 10

Example 2:y = 12x - 6y = -x + 1

Example 3:y = -x - 6y = 2x - 3

Homework