Textbook Question
Fill in the blank to correctly complete each sentence. The point (4,_____ ) lies on the graph of the equation y = 3x - 6.
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Ch. 2 - Graphs and Functions
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 3, Problem 2
Fill in the blank(s) to correctly complete each sentence. The graph of the line y= -2x+7 has slope ______ and y-intercept ______.
Verified step by step guidance1
Identify the slope-intercept form of a linear equation, which is given by \(y = mx + b\), where \(m\) represents the slope and \(b\) represents the y-intercept.
Compare the given equation \(y = -2x + 7\) to the slope-intercept form to determine the values of \(m\) and \(b\).
From the equation, observe that the coefficient of \(x\) is \(-2\), so the slope \(m\) is \(-2\).
Also, the constant term is \(7\), which means the y-intercept \(b\) is \(7\).
Therefore, the slope is \(-2\) and the y-intercept is \(7\).
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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, represented by the coefficient of x in the equation y = mx + b. It indicates how much y changes for a unit change in x. A negative slope means the line decreases as x increases.
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06:49
The Slope of a Line
Y-Intercept of a Line
The y-intercept is the point where the line crosses the y-axis, given by the constant term b in the equation y = mx + b. It represents the value of y when x is zero, providing a starting point for graphing the line.
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02:35Graphing Lines in Slope-Intercept Form
Slope-Intercept Form of a Linear Equation
The slope-intercept form y = mx + b expresses a linear equation clearly showing the slope (m) and y-intercept (b). This form makes it easy to identify key features of the line and to graph it quickly.
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03:56Slope-Intercept Form
Related Practice
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Fill in the blank(s) to correctly complete each sentence. The circle with center (3, 6) and radius 4 has equation _________.
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