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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 53
Chapter 3, Problem 53

Find the slope of each line, provided that it has a slope. 11x + 2y = 3

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1
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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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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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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Related Practice
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.

ƒ(x)=1−x2ƒ(x)=1-x^2

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Textbook Question

For each line, (a) find the slope and (b) sketch the graph. 2y = -3x

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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.

ƒ(x)=−x2ƒ(x)=-x^2

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Textbook Question

Find the slope of each line, provided that it has a slope. through (5, 6) and (5, -2)

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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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