4.6 Slope

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# 4.6 Slope - PowerPoint PPT Presentation

4.6 Slope. Objective: After studying this lesson you will be able to understand the concept of slope, relate the slope of a line to its orientation in the coordinate plane and recognize the relationships between slopes of parallel and perpendicular lines.

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## 4.6 Slope

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Presentation Transcript

### 4.6 Slope

Objective:

After studying this lesson you will be able to understand the concept of slope, relate the slope of a line to its orientation in the coordinate plane and recognize the relationships between slopes of parallel and perpendicular lines.

Definition The slope m of a nonvertical line, segment, or ray containing (x1, y1) and (x2, y2) is defined by the formula

Example. Find the slope of the segment joining (-2, 3) and (6, 5)

When the slope formula is applied to a vertical line such as line CD, the denominator is zero. Division by zero is undefined, so a vertical line has no slope.

C (6, 12)

D (6, 2)

A Visual Interpretation of Slope

Positive slope

Zero slope

Rising line

Horizontal line

Negative slope

No slope

Falling line

Vertical line

Theorem If two nonvertical lines are parallel, then their slopes are equal.

Theorem If the slopes of two nonvertical lines are equal, then the lines are parallel.

It can also be shown that there is a relationship between the slopes of two perpendicular lines—they are opposite reciprocals of each other.

example

Theorem If two lines are perpendicular and neither is vertical, each line’s slope is the opposite reciprocal of the other’s.

Theorem If a line’s slope is the opposite reciprocal of the another, the two lines are perpendicular.

You Try!

1. If A = (4, -6) and B = (-2, -8), find the slope of line AB.

2. Show that CEF is a right triangle

F (4, 7)

E (8, 4)

C (1, 3)

Given: ABE as shown

• Find: a. The slope of the altitude AC
• b. The slope of the median AD

A (-2, 10)

E (6, 5)

B (-4, 3)

Summary:

Describe how to find slope. How can you tell without graphing if lines are parallel? Perpendicular?

Homework: worksheet