Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used the ordered pairs (- 2, 2), (0, 0), and (2, 2) to graph a straight line.

검증된 단계별 안내

Identify the ordered pairs given in the problem: (-2, 2), (0, 0), and (2, 2). These represent points on the Cartesian coordinate plane.

Recall that a straight line has a constant slope. To determine if these points form a straight line, calculate the slope between each pair of points using the slope formula: m = (y₂ - y₁) / (x₂ - x₁).

First, calculate the slope between the points (-2, 2) and (0, 0): m = (0 - 2) / (0 - (-2)).

Next, calculate the slope between the points (0, 0) and (2, 2): m = (2 - 0) / (2 - 0).

Compare the slopes from the two calculations. If the slopes are equal, the points lie on the same straight line. If the slopes are not equal, the points do not form a straight line.

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주요 개념

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

Ordered Pairs

Ordered pairs are pairs of numbers used to represent points in a coordinate system, typically written as (x, y). The first number indicates the horizontal position (x-coordinate), while the second number indicates the vertical position (y-coordinate). Understanding how to plot these pairs is essential for graphing lines and interpreting their relationships.

Linear Equations

A linear equation represents a straight line in a coordinate plane and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. The relationship between the x and y values in ordered pairs must satisfy this equation for the points to lie on the same straight line. Recognizing whether a set of points forms a linear relationship is crucial for determining the validity of the statement.

Collinearity

Collinearity refers to the property of points lying on the same straight line. For three points to be collinear, the slope between any two pairs of points must be the same. In this case, checking if the ordered pairs (-2, 2), (0, 0), and (2, 2) are collinear involves calculating the slopes and confirming they are equal, which is key to validating the statement about graphing a straight line.