CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The point (4, ________) lies on the graph of the equation y = 3x - 6.

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Identify the given equation of the line: \(y = 3x - 6\).

Recognize that the point has an x-coordinate of 4, so substitute \(x = 4\) into the equation to find the corresponding y-coordinate.

Substitute \(x = 4\) into the equation: \(y = 3 \times 4 - 6\).

Simplify the right-hand side: \(y = 12 - 6\).

Calculate the value of \(y\) to find the missing coordinate of the point.

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Understanding Linear Equations

A linear equation like y = 3x - 6 represents a straight line on the coordinate plane. Each x-value corresponds to exactly one y-value, determined by substituting x into the equation. Recognizing this helps find missing coordinates on the line.

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Categorizing Linear Equations

Coordinate Points on a Graph

A point on a graph is represented as (x, y), where x is the horizontal position and y is the vertical position. To verify if a point lies on a graph, substitute the x-value into the equation and check if the resulting y matches the point's y-coordinate.

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Determining Different Coordinates for the Same Point

Substitution Method for Finding Coordinates

To find a missing coordinate, substitute the known x-value into the equation and solve for y. This method directly uses the equation to determine the corresponding y-value, ensuring the point lies on the graph.

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