Name:______Date:______Period:______

Accelerated Algebra I

Section 8-3 Day 2

I. Use the following directions for each problem to determine if the points are collinear or non-collinear.

1. Make a table of the coordinates in order of increasing x-coordinates.

2. Find the pattern of the x-coordinates and y-coordinates as you move from one point to the next.

3. For problems #1 & 2, plot the points on a coordinate plane.

4. Find the slope from point A to B, B to C, and A to C.

5. For problem #3, use the slope formula to find the slope between each pair of points.

1. A (3, 0), B (4, 2), C (5, 4). 2. A (-3, 7), B (0, 5), C (3, 3).

x / y
x / y

What is the pattern of the x-coordinates? _____What is the pattern of the x-coordinates? _____

What is the pattern of the y-coordinates? _____What is the pattern of the y-coordinates? _____

Slope A to B: _____ Slope A to B: _____

Slope B to C:_____ Slope B to C:_____

Slope A to C:_____ Slope A to C:_____

3. A (8, 1), B (6, 5), C (4, 9).

x / y

What is the pattern of the x-coordinates? _____

What is the pattern of the y-coordinates? _____

Slope A to B: _____

Slope B to C: _____

Slope A to C: _____

Write a conjecture comparing the relationship between slope and the pattern found in the change of x-coordinates and y-coordinates. ______

______

Collinear: ______

If points are collinear, then the slopes between any two points on the line are ______.

How to determine if points are collinear:

1. ______in order of increasing x-coordinates, if not already given.

2. Find the ______(vertical change).

3. Find the ______(horizontal change).

4. Is the ratio constant?

  • If yes, ______.
  • If no, ______.

Examples:

Determine whether the given points are collinear.

1. (1, 4), (3, 0), (5, -4)2. {(-5, 9), (-1, 1), (1, -4)}

3. 4. (5, -6), (2, -4), (-1, -7)

x / y
-2 / 7
3 / 2
8 / -3
x / y
-1 / 0
0 / -1
1 / -2
2 / -4

5. 6. (1, -1), (-1, 2), (-3, 5), (-5, 8)