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Give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. (x + 2)² + (y + 2)² = 4
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 3, Problema 46
In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. y = (2/5)x - 1
Guida verificata passo dopo passo1
Step 1: Recognize that the given equation is in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Step 2: Identify the slope (m) from the equation y = (2/5)x - 1. Here, m = 2/5. This means the line rises 2 units for every 5 units it moves to the right.
Step 3: Identify the y-intercept (b) from the equation y = (2/5)x - 1. Here, b = -1. This means the line crosses the y-axis at the point (0, -1).
Step 4: To graph the line, start by plotting the y-intercept (0, -1) on the coordinate plane. This is the starting point of the line.
Step 5: Use the slope (2/5) to find another point on the line. From (0, -1), move up 2 units and to the right 5 units to locate the next point. Draw a straight line through these points to complete the graph.
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Slope
The slope of a line measures its steepness and direction, represented as 'm' in the slope-intercept form of a linear equation, y = mx + b. It indicates how much y changes for a unit change in x. In the equation y = (2/5)x - 1, the slope is 2/5, meaning for every 5 units you move to the right on the x-axis, the line rises by 2 units.
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05:17
Types of Slope
Y-Intercept
The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the slope-intercept form y = mx + b. It indicates the value of y when x is zero. In the equation y = (2/5)x - 1, the y-intercept is -1, meaning the line crosses the y-axis at the point (0, -1).
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04:08Graphing Intercepts
Graphing Linear Equations
Graphing a linear equation involves plotting points that satisfy the equation and drawing a straight line through them. To graph y = (2/5)x - 1, start at the y-intercept (0, -1) and use the slope (2/5) to find another point. From (0, -1), move up 2 units and right 5 units to reach (5, 1), then draw the line through these points.
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06:00Categorizing Linear Equations
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