Domanda del libro di testo
Use the graph of y = f(x) to graph each function g. g(x) = f(-x)
961
views
Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 24
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = - 3/5, passing through (10, −4)
Guida verificata passo dopo passo1
Recall the point-slope form of a line equation: \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a point on the line.
Substitute the given slope \(m = -\frac{3}{5}\) and the point \((10, -4)\) into the point-slope form: \(y - (-4) = -\frac{3}{5}(x - 10)\).
Simplify the left side by changing \(y - (-4)\) to \(y + 4\), so the equation becomes \(y + 4 = -\frac{3}{5}(x - 10)\).
To write the equation in slope-intercept form $y = mx + b$, distribute the slope on the right side: \(y + 4 = -\frac{3}{5}x + \frac{3}{5} \times 10\).
Finally, isolate \(y\) by subtracting 4 from both sides: \(y = -\frac{3}{5}x + \frac{3}{5} \times 10 - 4\).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Point-Slope Form of a Line
The point-slope form is an equation of a line expressed as y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. It directly uses the given slope and point to write the line's equation.
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. After finding the equation in point-slope form, you can solve for y to rewrite it in slope-intercept form, identifying the y-intercept.
Video consigliato:
02:35Graphing Lines in Slope-Intercept Form
Slope of a Line
Slope measures the steepness of a line and is the ratio of vertical change to horizontal change between two points. A slope of -3/5 means the line falls 3 units vertically for every 5 units it moves horizontally to the right.
Video consigliato:
06:49The Slope of a Line
Pratica correlata
Domanda del libro di testo
The functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ-1 (x)) = = x and ƒ-1 (f(x)) = x. f(x) = (x +4)/(x-2)
603
views
Domanda del libro di testo
Use the graph of y = f(x) to graph each function g.
g(x) = f(-x)+1
684
views
Domanda del libro di testo
The functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ-1 (x)) = = x and ƒ-1 (f(x)) = x. f(x) = √x
695
views
Domanda del libro di testo
Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ is perpendicular to the line whose equation is 3x - 2y - 4 = 0 and has the same y-intercept as this line.
115
views
Domanda del libro di testo
In Exercises 11–26, determine whether each equation defines y as a function of x. xy - 5y =1
113
views