Fill in the blank(s) to correctly complete each sentence. The circle with equation has center with coordinates________ and radius equal to__________ .
Ch. 2 - Graphs and Functions

Chapter 3, Problem 2
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 guidance1
Identify the given equation of the graph: \(y = 3x - 6\).
Recognize that the point has an x-coordinate of 4, so substitute \(x = 4\) into the equation.
Calculate the corresponding y-coordinate by evaluating \(y = 3(4) - 6\).
Simplify the expression to find the value of \(y\).
Write the complete point as \((4, y)\) using the value found in the previous step.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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Standard Form of Line Equations
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.
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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.
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