Textbook Question
For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.
Ch. 2 - Graphs and Functions
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 3, Problem 53
Find the slope of each line, provided that it has a slope. 11x + 2y = 3
Verified step by step guidance1
Identify the given equation: \(11x + 2y = 3\).
Rewrite the equation in slope-intercept form \(y = mx + b\), where \(m\) represents the slope.
Isolate \(y\) by subtracting \$11x$ from both sides: \(2y = -11x + 3\).
Divide every term by 2 to solve for \(y\): \(y = \frac{-11}{2}x + \frac{3}{2}\).
Identify the slope \(m\) as the coefficient of \(x\), which is \(-\frac{11}{2}\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Slope of a Line
The slope of a line measures its steepness and direction, defined as the ratio of the change in y to the change in x (rise over run). It indicates how much y changes for a unit change in x and is usually denoted by 'm'.
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06:49
The Slope of a Line
Standard Form of a Linear Equation
A linear equation in standard form is written as Ax + By = C, where A, B, and C are constants. Understanding this form is essential because it can be rearranged to slope-intercept form to easily identify the slope.
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05:39Standard Form of Line Equations
Converting to Slope-Intercept Form
To find the slope from the standard form, rearrange the equation into slope-intercept form y = mx + b, where m is the slope. This involves isolating y on one side to express the equation explicitly in terms of x.
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03:56Slope-Intercept Form
Related Practice
Textbook Question
For each line, (a) find the slope and (b) sketch the graph. 2y = -3x
Textbook Question
For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.
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Textbook Question
Graph each function. Give the domain and range. ƒ(x)=-[[x]]
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Textbook Question
Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. g(-2)
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Textbook Question
Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (1, 6), perpendicular to 3x+5y=1
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