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Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
3장, 문제 38

In Exercises 37–40, find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (-1, -2) and (-3, -4)

검증된 단계별 안내
1
Step 1: Recall the formula for the slope of a line passing through two points (x₁, y₁) and (x₂, y₂): m = (y₂ - y₁) / (x₂ - x₁).
Step 2: Identify the coordinates of the two points given in the problem: Point 1 is (-1, -2) and Point 2 is (-3, -4). Assign x₁ = -1, y₁ = -2, x₂ = -3, and y₂ = -4.
Step 3: Substitute the values into the slope formula: m = ((-4) - (-2)) / ((-3) - (-1)). Simplify the numerator and denominator separately.
Step 4: Simplify the numerator: (-4) - (-2) becomes -4 + 2. Simplify the denominator: (-3) - (-1) becomes -3 + 1.
Step 5: Determine whether the slope is positive, negative, zero, or undefined. Based on the sign of the slope, decide whether the line rises, falls, is horizontal, or is vertical.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
1m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Slope of a Line

The slope of a line measures its steepness and direction, calculated as the change in the y-coordinates divided by the change in the x-coordinates between two points. It is represented by the formula m = (y2 - y1) / (x2 - x1). A positive slope indicates the line rises, while a negative slope indicates it falls.
추천 영상:
06:49
The Slope of a Line

Undefined Slope

A slope is considered undefined when the line is vertical, meaning the x-coordinates of the two points are the same. In this case, the formula for slope results in division by zero, which is mathematically undefined. Vertical lines do not rise or fall but run straight up and down.
추천 영상:
05:17
Types of Slope

Line Orientation

The orientation of a line can be categorized as rising, falling, horizontal, or vertical based on its slope. A rising line has a positive slope, a falling line has a negative slope, a horizontal line has a slope of zero, and a vertical line has an undefined slope. Understanding these orientations helps in visualizing the relationship between the points.
추천 영상:
06:49
The Slope of a Line