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

2. Graphs of Equations

Lines

College Algebra

2. Graphs of Equations

Lines

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1:29 minutes

Problem 72

Textbook Question

In Exercises 67–72, use intercepts to graph each equation. 6x-3y+15=0

Verified step by step guidance

Identify the equation given: \(6x - 3y + 15 = 0\).

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

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

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

Draw a straight line through the intercepts to graph the 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 when y=0, and the y-intercept occurs when x=0. For the equation 6x - 3y + 15 = 0, finding these intercepts helps in plotting the graph accurately.

Linear Equations

A linear equation represents a straight line when graphed on a coordinate plane. The general form is Ax + By + C = 0, where A, B, and C are constants. The equation given can be rearranged to slope-intercept form (y = mx + b) to identify the slope and y-intercept.

Graphing Techniques

Graphing techniques involve methods to visually represent equations on a coordinate plane. For linear equations, plotting the intercepts and using the slope to find additional points allows for an accurate representation of the line. Understanding these techniques is essential for effective graphing.