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), m = -2
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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
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- OLD 9. Conic Sections Coming soon
2. Graphs of Equations
Lines
Problem 15
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. through (-8,4), undefined slope
Verified step by step guidance1
Identify the key information: the line passes through the point (-8, 4) and has an undefined slope. An undefined slope means the line is vertical.
Recall that a vertical line has an equation of the form \(x = a\), where \(a\) is the x-coordinate of every point on the line.
Since the line passes through (-8, 4), the x-coordinate for all points on the line is -8.
Write the equation of the line as \(x = -8\).
Note that this equation is already in standard form because it cannot be expressed in slope-intercept form (which requires a defined slope).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Undefined Slope
An undefined slope occurs when a line is vertical, meaning it goes straight up and down. This happens because the change in x (horizontal change) is zero, making the slope formula (change in y divided by change in x) undefined. Such lines have equations of the form x = a constant.
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Types of Slope
Equation of a Vertical Line
A vertical line passing through a point (x, y) has an equation x = k, where k is the x-coordinate of the point. Since the slope is undefined, the line does not have a slope-intercept form (y = mx + b). The equation simply states that x is constant for all points on the line.
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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. For vertical lines, this form is useful because it can represent x = k as 1·x + 0·y = k. This form is often preferred for clarity and consistency in expressing linear equations.
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Standard Form of Line Equations
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