Textbook Question
Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (4, 7) and (8, 10)
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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 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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02:35Graphing Lines in Slope-Intercept Form
Related Practice
Textbook Question
Use the graph of y = f(x) to graph each function g.
g(x) = f(x)+1
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Textbook Question
Find the domain of each function. f(x)=3(x-4)
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Textbook Question
Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (2, 3) and (14, 8)
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