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

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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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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