Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−2, 6) and is perpendicular to the line whose equation is x = -4.
Table of contents
- 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 27
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. m=5, b=15
Verified step by step guidance1
Identify the given slope and y-intercept from the problem: slope \(m = 5\) and y-intercept \(b = 15\).
Recall the slope-intercept form of a line, which is given by the equation \(y = mx + b\).
Substitute the given values of \(m\) and \(b\) into the slope-intercept form to write the equation: \(y = 5x + 15\).
To write the equation in standard form, recall that the standard form of a line is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers and \(A \geq 0\).
Rearrange the slope-intercept form \(y = 5x + 15\) by moving all terms to one side to get \(-5x + y = 15\), then multiply both sides by \(-1\) to make \(A\) positive, resulting in \$5x - y = -15$.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Slope-Intercept Form of a Line
The slope-intercept form is expressed as y = mx + b, where m represents the slope and b is the y-intercept. This form clearly shows the rate of change and the point where the line crosses the y-axis, making it easy to graph and understand linear relationships.
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Graphing Lines in Slope-Intercept Form
Standard Form of a Line
Standard form of a linear equation is written as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is useful for analyzing and solving systems of equations and is often required for final answers in algebra problems.
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Standard Form of Line Equations
Interpreting Slope and Y-Intercept
The slope (m) indicates the steepness and direction of a line, showing how much y changes for a unit change in x. The y-intercept (b) is the point where the line crosses the y-axis (x=0). Understanding these helps in writing and graphing the equation of a line from given values.
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Slope-Intercept Form
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