Math Problem Statement
Solution
To solve the problem, we need to find the angle that the line makes with the positive x-axis.
Steps:
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Find the slope of the line: The equation of the line is given in general form . To convert it to slope-intercept form , solve for :
The slope is .
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Use the slope to find the angle: The angle that the line makes with the positive x-axis can be found using the formula:
Taking the arctangent of both sides:
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Calculate the angle:
Let me compute this.
The angle that the line makes with the positive x-axis is approximately , which is closest to option A: .
Would you like more details on this solution or have any other questions?
Here are five related questions to explore:
- How do you derive the slope-intercept form from the general form of a line?
- What is the relationship between slope and angle for a line?
- How can you calculate the angle if the slope is negative or positive?
- Why is the arctangent function used to find the angle from the slope?
- How would the answer change if the slope were steeper?
Tip: For any line, the angle with the x-axis can be found directly from its slope using the inverse tangent function.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Trigonometry
Formulas
Slope of a line: m = -A/B
tan(θ) = |m|
θ = arctan(m)
Theorems
Slope-Intercept Form Theorem
Inverse Tangent Function
Suitable Grade Level
Grades 9-12
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