Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
2. Graphs of Equations
Lines
1:54 minutes
Problem 46
Textbook Question
Textbook QuestionIn 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
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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. In this equation, 'm' indicates how much y changes for a unit change in x. A positive slope means the line rises as it moves from left to right, while a negative slope indicates it falls.
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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. This value indicates the output (y) when the input (x) is zero. For 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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Graphing 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 by plotting the y-intercept at (0, -1), then use the slope of 2/5 to find another point by moving up 2 units and right 5 units. Connecting these points gives the visual representation of the line.
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Categorizing Linear Equations
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