Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

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0:55 minutes

Problem 2

Textbook Question

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: \( y = 3x - 6 \).

Substitute the x-coordinate of the point into the equation: \( x = 4 \).

Calculate the value of y by substituting \( x = 4 \) into the equation: \( y = 3(4) - 6 \).

Simplify the expression to find the value of y.

The y-coordinate of the point (4, y) is the result of the simplification.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.