Textbook Question
Determine whether each function is even, odd, or neither. ƒ(x)=x4-5x+8
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Ch. 2 - Graphs and Functions
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 3, Problem 62
For each line described, write an equation in
(a)slope-intercept form, if possible, and
(b)standard form.
through and
Verified step by step guidance1
First, find the slope \( m \) of the line passing through the points \((-2, 4)\) and \((1, 3)\) using the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 4}{1 - (-2)} \].
Simplify the slope expression to get the value of \( m \).
Use the point-slope form of a line equation with one of the points, for example \((-2, 4)\), and the slope \( m \): \[ y - y_1 = m(x - x_1) \].
Rewrite the equation from point-slope form into slope-intercept form \( y = mx + b \) by solving for \( y \) and simplifying.
Convert the slope-intercept form into standard form \( Ax + By = C \) by rearranging terms so that \( x \) and \( y \) are on one side and the constant on the other, ensuring \( A, B, C \) are integers and \( A \) is non-negative.
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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 measures the steepness of a line and is calculated as the change in y-values divided by the change in x-values between two points. For points (-2, 4) and (1, 3), slope = (3 - 4) / (1 - (-2)) = -1/3. Understanding slope is essential for writing the equation of a line.
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The Slope of a Line
Slope-Intercept Form
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. After finding the slope, substitute one point to solve for b. This form clearly shows the slope and where the line crosses the y-axis.
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03:56Slope-Intercept Form
Standard Form of a Line
The standard form of a line is Ax + By = C, where A, B, and C are integers, and A ≥ 0. It is another way to express linear equations, often used for solving systems or graphing. Converting from slope-intercept form involves rearranging terms and clearing fractions.
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Related Practice
Textbook Question
Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. g(-x)
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Textbook Question
Graph the line passing through the given point and having the indicated slope. Plot two points on the line. through (- 5/2 , 3), undefined slope
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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. ƒ(x+2)
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Textbook Question
Graph the line passing through the given point and having the indicated slope. Plot two points on the line. through ( - 1/2 , 4), m = 0
Textbook Question
Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5.