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 of the graph: \(y = 3x - 6\).
2. Recognize that the point has an x-coordinate of 4, so substitute \(x = 4\) into the equation.
3. Calculate the corresponding y-coordinate by evaluating \(y = 3(4) - 6\).
4. Simplify the expression to find the value of \(y\).
5. Write the complete point as \((4, y)\) using the value found in the previous step.

Key Concepts

Understanding the Equation of a Line

The equation y = 3x - 6 represents a linear function where y depends on x. It shows that for any x-value, y can be found by multiplying x by 3 and then subtracting 6. This relationship forms a straight line on the coordinate plane.

Substitution Method

To find a missing coordinate on a graph, substitute the known x-value into the equation to solve for y. This method allows you to determine the corresponding y-value that satisfies the equation for the given x.

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. For a point to lie on a graph of an equation, its coordinates must satisfy the equation.