Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-1,3), and (3,4)
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- 0. Review of Algebra4h 18m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations1h 43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 5m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 22m
- 10. Combinatorics & Probability1h 45m
- Appendix 1. Review of Real Numbers2h 24m
- Appendix 2. Linear Equations and Inequalities3h 42m
- OLD 9. Sequences, Induction, and Probability Coming soon
- 1. - OLD - Fundamental Concepts of Algebra Coming soon
- 2. - OLD - Equations and Inequalities Coming soon
- OLD 4. Rational Functions Coming soon
- OLD 2. Functions & Graphs Coming soon
- OLD 6. Exponential and Logarithmic Functions Coming soon
- OLD 7. Systems of Equations and Inequalities Coming soon
- OLD 8. Matrices and Determinants Coming soon
- OLD 9. Conic Sections Coming soon
2. Graphs of Equations
Lines
Problem 25
Textbook Question
Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. horizontal, through (-7,4)
Verified step by step guidance1
Identify the type of line described: a horizontal line has a slope of 0, meaning it does not rise or fall as it moves along the x-axis.
Recall that the equation of a horizontal line is always of the form \(y = k\), where \(k\) is the constant y-value for all points on the line.
Since the line passes through the point \((-7, 4)\), the y-value for every point on the line is 4.
Write the equation of the line as \(y = 4\).
Note that this equation is already in slope-intercept form \(y = mx + b\) with \(m = 0\) and \(b = 4\), and it can also be considered in standard form as \$0x + y = 4$.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Equation of a Horizontal Line
A horizontal line has a constant y-value for all x-values, meaning its slope is zero. The equation of a horizontal line is written as y = k, where k is the y-coordinate of any point on the line. For example, a horizontal line through (-7, 4) is y = 4.
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Standard Form of Line Equations
Standard Form of a Linear Equation
The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A ≥ 0. This form is useful for quickly identifying intercepts and is often required for certain exercises. For horizontal lines, the standard form is typically y = constant, which can be rewritten as 0x + 1y = constant.
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Standard Form of Line Equations
Slope-Intercept Form of a Linear Equation
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. It clearly shows the slope and where the line crosses the y-axis. For horizontal lines, the slope m = 0, so the equation simplifies to y = b, making it easy to write and interpret.
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Slope-Intercept Form
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