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.

Verified step by step guidance

1. Identify the equation given: \( y = 3x - 6 \).
2. Substitute the x-coordinate of the point into the equation: \( y = 3(4) - 6 \).
3. Simplify the expression: calculate \( 3 \times 4 \) and then subtract 6.
4. The result of the simplification gives the y-coordinate of the point.
5. Fill in the blank with the calculated y-coordinate to complete the point (4, y).

Key Concepts

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The general form is y = mx + b, where m is the slope and b is the y-intercept. Understanding this form is essential for determining the relationship between x and y values in a graph.

Substituting Values

Substituting values involves replacing a variable in an equation with a specific number to find the corresponding output. In this case, substituting x = 4 into the equation y = 3x - 6 allows us to calculate the y-coordinate of the point on the graph, which is crucial for completing the sentence.

Graphing Points

Graphing points involves plotting coordinates on a Cartesian plane, where the x-coordinate indicates the horizontal position and the y-coordinate indicates the vertical position. Understanding how to graph points is vital for visualizing the relationship defined by the linear equation and confirming that the point lies on the graph.