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)
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
Rewrite the given equation 3x - 2y - 4 = 0 in slope-intercept form (y = mx + b) by isolating y. Start by moving the terms involving x and the constant to the other side: -2y = -3x + 4.
Divide through by -2 to solve for y: y = (3/2)x - 2. This gives the slope (m) of the given line as 3/2 and the y-intercept (b) as -2.
Recall that perpendicular lines have slopes that are negative reciprocals of each other. The slope of the new line will be the negative reciprocal of 3/2, which is -2/3.
Since the new line has the same y-intercept as the given line, the y-intercept (b) remains -2.
Write the equation of the new line in slope-intercept form using the slope (-2/3) and y-intercept (-2): 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)
Textbook Question
Use the graph of y = f(x) to graph each function g. g(x) = f(-x)
1
views
Textbook Question
Find the midpoint of each line segment with the given endpoints. (-3, -4) and (6, −8)
1
views
Textbook Question
In Exercises 11–26, determine whether each equation defines y as a function of x. xy - 5y =1
Textbook Question
Determine whether the graph of each equation is symmetric with respect to the y-axis, the x-axis, the origin, more than one of those, or none of these. x^2 + y^2 =17