Skip to main content
Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 8th EditionCh. 2 - Functions and Graphs문제 43
3장, 문제 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.

검증된 단계별 안내
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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m
도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.
추천 영상:
가이드 코스
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.
추천 영상:
가이드 코스
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.
추천 영상:
가이드 코스
07:52
Parallel & Perpendicular Lines
관련 실천
교과서 질문

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
교과서 질문

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
교과서 질문

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
교과서 질문

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
교과서 질문

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

635
views
교과서 질문

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

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

914
views