Textbook Question
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)
99
views
Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
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
Chapter 3, Problem 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.
Verified step by step guidance1
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.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
Recommended video:
Guided course
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.
Recommended video:
Guided course
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.
Recommended video:
Guided course
04:08Graphing Intercepts
Related Practice
Textbook Question
Find the domain of each function. f(x) = √(24 - 2x)
942
views
Textbook Question
Use the graph of y = f(x) to graph each function g. g(x) = f(-x)
960
views
Textbook Question
Find the midpoint of each line segment with the given endpoints. (-3, -4) and (6, −8)
840
views
Textbook Question
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
Textbook Question
In Exercises 11–26, determine whether each equation defines y as a function of x. xy - 5y =1
113
views