Textbook Question
Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. x² + y² = 16, x-y = 4
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 3, Problem 68
Use intercepts to graph each equation. 6x-9y-18 = 0
Verified step by step guidance1
Rewrite the given equation in standard form: \(6x - 9y - 18 = 0\).
Find the x-intercept by setting \(y = 0\) in the equation and solving for \(x\). This means solving \(6x - 9(0) - 18 = 0\) for \(x\).
Find the y-intercept by setting \(x = 0\) in the equation and solving for \(y\). This means solving \(6(0) - 9y - 18 = 0\) for \(y\).
Plot the intercept points found on the coordinate plane: the x-intercept on the x-axis and the y-intercept on the y-axis.
Draw a straight line through the two intercept points 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.
Finding x-intercept
The x-intercept is the point where the graph crosses the x-axis, meaning y = 0. To find it, substitute y = 0 into the equation and solve for x. This gives a coordinate of the form (x, 0), which helps in plotting the graph.
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04:08
Graphing Intercepts
Finding y-intercept
The y-intercept is the point where the graph crosses the y-axis, meaning x = 0. To find it, substitute x = 0 into the equation and solve for y. This results in a coordinate of the form (0, y), which is essential for graphing the line.
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04:08Graphing Intercepts
Graphing a linear equation using intercepts
Once the x- and y-intercepts are found, plot these points on the coordinate plane. Drawing a straight line through these two points represents the graph of the linear equation. This method is a straightforward way to graph lines without needing slope.
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