CHAPTER 3.4

HOW DO YOU FIND THE SLOPES OF A LINE GIVEN THE COORDINATES

OF TWO POINTS ON A LINE? 

LINES AND SLOPE

Any linear line has a constant slope.

The slope is found by calculating the ratio of the rise and run.

There are 2 methods to find slope, graphically and algebraically.

TYPES OF SLOPE

Negative slope: falls to the right

Positive slope: rises to the right

Zero slope: looks like a horizontal line

Undefined slope: looks like a vertical line

SLOPE: ALGEBRAICALLY

To find slope algebraically you use the formula for slope:

You will be given 2 points then plug them into the formula.

(9, 4) and (11, 7)

12

12

xx

yym

2

3

911

47

12

12

xx

yym

FIND THE SLOPES OF THE FOLLOWING

(0, 5) and (2, 7)

(-2, 1) and (-5, -3)

(0, 0) and (3, 4)

SLOPE GRAPHICALLY

Count out the rise, then count out the run and divide.

SLOPE GRAPHICALLY

SLOPE GRAPHICALLY

SLOPE PACKET

PARALLEL LINES AND SLOPE

Lines that are parallel have the same slope.

PERPENDICULAR LINES AND SLOPE

Perpendicular lines have a negative reciprocal slope.

PARALLEL VS PERPENDICULAR

22

1 xy

2

1m

15 xy 5m

14

3

xy

4

3m

207

5

xy

7

5m

21

2m

5

1m

3

4m

5

7m

DETERMINING WHETHER LINES ARE PARALLEL, PERPENDICULAR,

OR NEITHER FROM SLOPE

Is the line AB that passes through the points A(1, 0) and B(5, 3) parallel, perpendicular, or neither to the line CD that passes through C(6, -1) and D(0, 2)

DETERMINING WHETHER LINES ARE PARALLEL, PERPENDICULAR,

OR NEITHER FROM SLOPE

Is the line HI that passes through the points H(5, 1) and I(-1, -1) parallel, perpendicular, or neither to the line JK that passes through J(2, 1) and K(3, -2)

PAGE 175

#7 – 9, 13 – 15, 19 - 21

GRAPHING LINES THAT ARE PARALLEL

GRAPH A LINE PARALLEL TO LINE AB

GRAPH A LINE PERPENDICULAR TO THE LINE AND THAT PASSES

THROUGH POINT P

GRAPH A LINE PERPENDICULAR TO THE LINE AND THAT PASSES

THROUGH POINT P