Skip to main content
Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 2 - Functions and GraphsProblema 43
Capitolo 3, Problema 43

In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (4, -7) and parallel to the line whose equation is 3x + y - 9 = 0.

Guida verificata passo dopo passo
1
Rewrite the given line equation 3x + y - 9 = 0 in slope-intercept form (y = mx + b) by isolating y. Subtract 3x and add 9 to both sides to get y = -3x + 9. Here, the slope (m) of the given line is -3.
Since the new line is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also m = -3.
Use the point-slope form of a line equation, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. Substitute the point (4, -7) and the slope m = -3 into the formula: y - (-7) = -3(x - 4).
Simplify the point-slope form equation: y + 7 = -3(x - 4). Expand the right-hand side to get y + 7 = -3x + 12.
Convert the equation into slope-intercept form (y = mx + b) by isolating y. Subtract 7 from both sides to get y = -3x + 5. The final equations are: Point-slope form: y + 7 = -3(x - 4), and Slope-intercept form: y = -3x + 5.

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:
3m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Point-Slope Form

Point-slope form is a way to express the equation of a line given a point on the line and its slope. The formula is written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is particularly useful for quickly writing the equation of a line when you know a specific point and the slope.
Video consigliato:
05:46
Point-Slope Form

Slope-Intercept Form

Slope-intercept form is another way to express the equation of a line, defined as y = mx + b, where m is the slope and b is the y-intercept. This form allows for easy identification of the slope and where the line crosses the y-axis. Converting from point-slope to slope-intercept form is a common task in algebra.
Video consigliato:
03:56
Slope-Intercept Form

Parallel Lines

Parallel lines are lines in a plane that never intersect and have the same slope. When writing the equation of a line parallel to another, it is essential to use the same slope as the given line. In this case, the slope can be derived from the standard form of the line's equation, allowing for the creation of a new line that maintains the same direction.
Video consigliato:
07:52
Parallel & Perpendicular Lines
Pratica correlata
Domanda del libro di testo

Give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. (x − 3)² + (y + 1)² = 36

811
views
Domanda del libro di testo

Give the slope and y-intercept of each line whose equation is given. Then graph the linear function. f(x) = (3/4)x-2

123
views
Domanda del libro di testo

Find f+gf+g, f−gf-g, fgfg, and fg\(\frac{f}{g}\). Determine the domain for each function.

f(x)=6−1xf\(\left\)(x\(\right\))=6-\(\frac{1}{x}\), g(x)=1xg\(\left\)(x\(\right\))=\(\frac{1}{x}\)

578
views
Domanda del libro di testo

In Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range off and ƒ¯¹. f(x) = (x − 1)², x ≤ 1

637
views
Domanda del libro di testo

Use the graph of y = f(x) to graph each function g. g(x) = (1/2)f(2x)

635
views
Domanda del libro di testo

Find ƒ+g and determine the domain for each function.

f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)

914
views