교과서 질문
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)
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- 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
3장, 문제 23a
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.
검증된 단계별 안내1
Step 1: Identify the slope of the given line. Rewrite the equation 3x - 2y - 4 = 0 in slope-intercept form (y = mx + b) to find its slope.
Step 2: Rearrange the equation to solve for y. Start by adding 2y to both sides to get 3x - 4 = 2y.
Step 3: Divide every term by 2 to isolate y, resulting in y = (3/2)x - 2. The slope (m) of this line is 3/2.
Step 4: Determine the slope of the line perpendicular to the given line. The slope of a line perpendicular to another is the negative reciprocal of the original slope. Therefore, the perpendicular slope is -2/3.
Step 5: Use the y-intercept from the original line, which is -2, to write the equation of the new line in slope-intercept form: y = (-2/3)x - 2.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Slope-Intercept Form
The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b represents the y-intercept. This form is useful for quickly identifying the slope of the line and where it crosses the y-axis, making it easier to graph linear functions.
추천 영상:
가이드 코스
03:56
Slope-Intercept Form
Perpendicular Lines
Two lines are perpendicular if the product of their slopes is -1. This means that if one line has a slope of m, the other line will have a slope of -1/m. Understanding this relationship is crucial for finding the slope of a line that is perpendicular to a given line.
추천 영상:
가이드 코스
07:52Parallel & Perpendicular Lines
Finding the Y-Intercept
The y-intercept of a line is the point where the line crosses the y-axis, which occurs when x = 0. To find the y-intercept from a linear equation, you can rearrange the equation into slope-intercept form or directly substitute x = 0 into the equation. This value is essential for constructing the equation of a line with a specific y-intercept.
추천 영상:
가이드 코스
04:08Graphing Intercepts
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