Textbook Question
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = −1, passing through (−4, − 1/4)
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
Chapter 3, Problem 21
Find the midpoint of each line segment with the given endpoints. (-2, -8) and (−6, −2)
Verified step by step guidance1
Recall the midpoint formula for a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\):
\[\text{Midpoint} = \left( \frac{\,x_1 + x_2}{2}, \frac{\,y_1 + y_2}{2} \right)\]
Identify the coordinates of the given endpoints:
\(x_1 = -2, y_1 = -8\) and \(x_2 = -6, y_2 = -2\).
Substitute the values into the midpoint formula:
\[\left( \frac{-2 + (-6)}{2}, \frac{-8 + (-2)}{2} \right)\]
Simplify the expressions inside the parentheses by performing the addition in the numerators:
\[\left( \frac{-2 - 6}{2}, \frac{-8 - 2}{2} \right)\]
Calculate the final coordinates of the midpoint by dividing each sum by 2:
\[\left( \frac{-8}{2}, \frac{-10}{2} \right)\]
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Coordinate Plane and Points
The coordinate plane is a two-dimensional system where each point is identified by an ordered pair (x, y). Understanding how to plot and interpret points is essential for visualizing line segments and their properties.
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Graphs & the Rectangular Coordinate System
Line Segment
A line segment is the part of a line bounded by two endpoints. Knowing the endpoints allows us to analyze properties like length and midpoint, which are fundamental in coordinate geometry.
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06:49The Slope of a Line
Midpoint Formula
The midpoint formula calculates the point exactly halfway between two endpoints. It is given by ((x1 + x2)/2, (y1 + y2)/2), averaging the x-coordinates and y-coordinates separately to find the midpoint.
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Related Practice
Textbook Question
Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−6, 4) and is perpendicular to the line that has an x intercept of 2 and a y-intercept of -4.
Textbook Question
Use the graph of y = f(x) to graph each function g. g(x) = f(x+1)
Textbook Question
Use the graph of y = f(x) to graph each function g.
g(x) = f(x-1)+2
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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) = 1/x
Textbook Question
Find the domain of each function. f(x) = √(5x+35)