Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Lines

College Algebra

2. Graphs of Equations

Lines

1:29 minutes

Problem 68b

Textbook Question

In Exercises 67–72, use intercepts to graph each equation. 6x-9y-18 = 0

Verified step by step guidance

To find the x-intercept, set \( y = 0 \) in the equation \( 6x - 9y - 18 = 0 \) and solve for \( x \).

To find the y-intercept, set \( x = 0 \) in the equation \( 6x - 9y - 18 = 0 \) and solve for \( y \).

Plot the x-intercept and y-intercept on the coordinate plane.

Draw a straight line through the two intercepts to graph the equation.

Verify the line by checking if another point on the line satisfies the original equation.

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Key Concepts

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

Intercepts

Intercepts are points where a graph intersects the axes. The x-intercept occurs where the graph crosses the x-axis (y=0), and the y-intercept occurs where it crosses the y-axis (x=0). Finding these points is essential for graphing linear equations, as they provide key coordinates that define the line's position.

Linear Equations

A linear equation is an equation of the first degree, meaning it can be expressed in the form Ax + By + C = 0, where A, B, and C are constants. The graph of a linear equation is a straight line, and understanding its structure helps in identifying its slope and intercepts, which are crucial for graphing.

Graphing Techniques

Graphing techniques involve methods used to visually represent equations on a coordinate plane. For linear equations, the most common technique is to plot the intercepts and then draw a straight line through these points. This approach simplifies the graphing process and ensures accuracy in representing the equation.