Textbook Question
Determine whether each relation is a funciton, Give the domain and range for each relation. (1, 10), (2, 500), (13, π)
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 1
Write an equation for line L in point-slope form and slope-intercept form.
Verified step by step guidance1
Identify the slope of the given line y = 3x + 2. Since the equation is in slope-intercept form y = mx + b, the slope m is 3.
Since line L is parallel to y = 3x + 2, it has the same slope. So, the slope of line L is also 3.
Use the point-slope form of a line equation, which is \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is a point on the line and m is the slope. Here, the point is (-1, 2) and the slope is 3.
Substitute the point (-1, 2) and slope 3 into the point-slope form: \(y - 2 = 3(x - (-1))\) or \(y - 2 = 3(x + 1)\).
To write the equation in slope-intercept form, simplify the point-slope form by distributing the slope and solving for y: \(y - 2 = 3x + 3\), then add 2 to both sides to get \(y = 3x + 5\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Slope of Parallel Lines
Parallel lines have the same slope. Since line L is parallel to y = 3x + 2, it shares the slope of 3. This means the rate of change for line L is identical to the given line, which is essential for writing its equation.
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Parallel & Perpendicular Lines
Point-Slope Form of a Line
The point-slope form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. This form is useful when you know a point on the line and its slope, allowing you to write the equation directly from given information.
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05:46Point-Slope Form
Slope-Intercept Form of a Line
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. After finding the slope and using a point to solve for b, this form provides a clear way to express the line's equation and easily graph it.
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Related Practice
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