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
2:20 minutes
Problem 45aLial - 13th Edition
Textbook Question
Textbook QuestionFind the slope of the line satisfying the given conditions. See Example 5. through (5, 9) and (-2, 9)
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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, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. It is often represented as 'm' in the slope-intercept form of a linear equation, y = mx + b. A positive slope indicates the line rises from left to right, while a negative slope indicates it falls.
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Coordinate Points
Coordinate points are pairs of numbers that define a position in a two-dimensional space, typically written as (x, y). In this context, the points (5, 9) and (-2, 9) represent specific locations on the Cartesian plane. Understanding how to interpret these points is crucial for calculating the slope between them.
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Formula for Slope
The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is given by m = (y2 - y1) / (x2 - x1). This formula allows you to find the slope by substituting the y-coordinates and x-coordinates of the two points. In this case, substituting the coordinates (5, 9) and (-2, 9) will yield the slope of the line connecting these points.
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Textbook Question
In Exercises 1–4, write an equation for line L in point-slope form and slope-intercept form.
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