Fill in the blank 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 given equation: \( y = 3x - 6 \).
2. Substitute the x-coordinate of the point into the equation: \( x = 4 \).
3. Calculate the value of y by substituting \( x = 4 \) into the equation: \( y = 3(4) - 6 \).
4. Simplify the expression to find the value of y.
5. The y-coordinate of the point (4, y) is the result of the simplification.

Key Concepts

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed on a coordinate plane. It is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. Understanding linear equations is essential for determining the relationship between x and y values in a given equation.

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. This process is fundamental in solving equations and finding specific points on a line.

Coordinate System

A coordinate system is a two-dimensional plane defined by a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on this plane is represented by an ordered pair (x, y), where x indicates the position along the x-axis and y indicates the position along the y-axis. Understanding the coordinate system is crucial for graphing equations and interpreting their geometric representations.