Match each equation with the sketch that most closely resembles its graph. y = 5

검증된 단계별 안내

Recognize that the equation \(y = 5\) represents a horizontal line because it is in the form \(y = c\), where \(c\) is a constant.

Understand that for every value of \(x\), the value of \(y\) remains constant at 5, so the graph is a straight line parallel to the x-axis.

Identify that the line will cross the y-axis at the point \((0, 5)\), which is the y-intercept.

Note that the slope of the line is 0, meaning there is no rise or fall as you move along the x-axis.

Match the equation \(y = 5\) with the sketch that shows a horizontal line passing through the y-coordinate 5.

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주요 개념

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

Horizontal Lines

A horizontal line is a straight line where all points have the same y-coordinate. Its equation is of the form y = k, where k is a constant. For y = 5, the line passes through all points with y-coordinate 5, parallel to the x-axis.

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy the equation and connecting them. For equations like y = 5, the graph is a straight line. Understanding how to interpret and sketch these lines is essential for matching equations to their graphs.

Coordinate Plane and Axes

The coordinate plane consists of the x-axis (horizontal) and y-axis (vertical). Knowing how to locate points and lines relative to these axes helps in visualizing graphs. For y = 5, the line is parallel to the x-axis and crosses the y-axis at 5.