Find the slope of each line, provided that it has a slope. through (5, 6) and (5, -2)

검증된 단계별 안내

Recall that the slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula: \[m = \frac{y_2 - y_1}{x_2 - x_1}\]

Identify the coordinates of the two points given: \((x_1, y_1) = (5, 6)\) and \((x_2, y_2) = (5, -2)\).

Substitute the coordinates into the slope formula: \[m = \frac{-2 - 6}{5 - 5}\]

Simplify the numerator and denominator separately: Numerator: \(-2 - 6 = -8\) Denominator: \(5 - 5 = 0\)

Interpret the result: since the denominator is zero, the slope is undefined, which means the line is vertical and does not have a defined slope.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

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 is calculated as the ratio of the change in y-values to the change in x-values between two points. It is given by the formula m = (y2 - y1) / (x2 - x1). A positive slope means the line rises, while a negative slope means it falls.

Vertical Lines and Undefined Slope

A vertical line has the same x-coordinate for all points, resulting in zero change in x. Since slope involves division by the change in x, this leads to division by zero, which is undefined. Therefore, vertical lines do not have a defined slope.

Coordinates of Points

Points on the coordinate plane are represented as (x, y). Understanding how to use these coordinates to find differences in x and y values is essential for calculating slope. In this problem, the points (5, 6) and (5, -2) share the same x-value, indicating a vertical line.