Domanda del libro di testo
In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(-3, -3), (-2, −2), (−1, −1), (0, 0)}
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 3, Problema 7
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (2, −3) and perpendicular to the line whose equation is y = (1/5)x + 6
Guida verificata passo dopo passo1
Identify the slope of the given line from its equation \(y = \frac{1}{5}x + 6\). The slope is the coefficient of \(x\), which is \(\frac{1}{5}\).
Determine the slope of the line perpendicular to the given line. Recall that perpendicular slopes are negative reciprocals, so the new slope will be \(-5\) (since \(-\frac{1}{\frac{1}{5}} = -5\)).
Use the point-slope form of a line equation, which is \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is the given point. Substitute \(m = -5\) and the point \((2, -3)\) to get \(y - (-3) = -5(x - 2)\).
Simplify the point-slope form equation to \(y + 3 = -5(x - 2)\), which is the required point-slope form of the line.
Convert the point-slope form to slope-intercept form by distributing and isolating \(y\): \(y + 3 = -5x + 10\), then subtract 3 from both sides to get \(y = -5x + 7\).
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Point-Slope Form of a Line
The point-slope form is an equation of a line expressed as y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. It is useful for writing the equation when a point and slope are known.
Video consigliato:
05:46
Point-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. This form clearly shows the slope and where the line crosses the y-axis, making it easy to graph and interpret.
Video consigliato:
02:35Graphing Lines in Slope-Intercept Form
Perpendicular Slopes
Two lines are perpendicular if their slopes are negative reciprocals, meaning m₁ * m₂ = -1. Given a slope m, the slope of a perpendicular line is -1/m, which helps find the slope of the required line.
Video consigliato:
07:52Parallel & Perpendicular Lines
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