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Ch. 1 - Functions
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Briggs 3rd EditionCh. 1 - Functions문제 17
1장, 문제 17

Find the linear function whose graph passes through the point (3, 2) and is parallel to the line y=3x+8y= 3x + 8 .

검증된 단계별 안내
1
Identify the slope of the given line, which is parallel to the line we need to find. The given line is \( y = 3x + 8 \), so the slope \( m \) is 3.
Use the point-slope form of a linear 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.
Substitute the point \( (3, 2) \) and the slope \( m = 3 \) into the point-slope form: \( y - 2 = 3(x - 3) \).
Simplify the equation to get it into the slope-intercept form \( y = mx + b \).
Distribute the 3 on the right side: \( y - 2 = 3x - 9 \), then add 2 to both sides to solve for \( y \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
4m
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주요 개념

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

Linear Functions

A linear function is a mathematical expression that describes a straight line when graphed. It is typically represented in the form y = mx + b, where m is the slope and b is the y-intercept. Understanding linear functions is crucial for determining the relationship between variables and for solving problems involving lines.
추천 영상:
가이드 코스
07:17
Linearization

Slope

The slope of a line measures its steepness and direction, calculated as the change in y divided by the change in x (rise over run). For two parallel lines, the slopes are equal. In this question, the slope of the given line y = 3x + 8 is 3, which will be the same for the linear function we need to find.
추천 영상:
3:56
Slope-Intercept Form

Point-Slope Form

The point-slope form of a linear equation is expressed as y - y1 = m(x - x1), where (x1, y1) is a specific point on the line and m is the slope. This form is particularly useful for writing the equation of a line when you know a point on the line and its slope, allowing for straightforward calculations in this problem.
추천 영상:
3:56
Slope-Intercept Form
관련 실천
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