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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