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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 52
Chapter 3, Problem 52

For each line, (a) find the slope and (b) sketch the graph. y = 2x - 4

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Identify the equation of the line given: \(y = 2x - 4\).
Recall that the equation is in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Compare the given equation to the slope-intercept form to find the slope \(m\). Here, \(m = 2\).
To sketch the graph, start by plotting the y-intercept point \((0, -4)\) on the coordinate plane.
From the y-intercept, use the slope \(m = 2\) (which means rise over run = 2/1) to find another point by moving up 2 units and right 1 unit, then draw the line through these points.

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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 and direction of a line, calculated as the ratio of the change in y to the change in x (rise over run). For a line in the form y = mx + b, the slope is the coefficient m. In y = 2x - 4, the slope is 2, indicating the line rises 2 units vertically for every 1 unit it moves horizontally.
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The Slope of a Line

Slope-Intercept Form of a Line

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. This form makes it easy to identify the slope and where the line crosses the y-axis. For y = 2x - 4, the y-intercept is -4, meaning the line crosses the y-axis at (0, -4).
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Graphing Lines in Slope-Intercept Form

Graphing Linear Equations

Graphing a linear equation involves plotting the y-intercept and using the slope to find additional points. Starting at (0, b), move vertically and horizontally according to the slope to plot points, then draw a straight line through them. This visualizes the relationship between x and y defined by the equation.
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Categorizing Linear Equations
Related Practice
Textbook Question

Find the value of the function for the given value of x.

f(x)={3if 0<x≤410−2[[5−x]]if x>4, for , for x=6.2f(x)=\(\begin{cases}\)3 & \(\text{if }\)0<x\(\leq\)4\\ 10-2[\(\left\]\lbrack\)5-x]\(\right\[\rbrack\) & \(\text{if }\)x>4,\(\text{ for }\]\end{cases}\),\(\text{ for }\)x=6.2

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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

Textbook Question

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

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(0)

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(-3)

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Textbook Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y=√(x-3)