Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 2

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 guidance

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.

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.

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Graphs and Coordinates - Example

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