Math Problem Statement
The equation of line AB is given as y=3x+4. Determine which of the following lines are parallel to line AB. Select all suitable options. Option A: 3y=12x+6 Option B: 4y=12x+5 Option C: y=4x+4 Option D: y=6x+8 Option E: 6x-2y=10
Solution
To determine which lines are parallel to the line given by the equation , we need to compare the slopes of the given lines with the slope of line .
Step 1: Identify the slope of line
The equation of line is . The slope-intercept form of a line is given by , where is the slope.
For line :
- Slope () = 3
Step 2: Find the slope of each option
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Option A:
- Slope () = 4
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Option B:
- Slope () = 3
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Option C:
- Slope () = 4
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Option D:
- Slope () = 6
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Option E: \text{Rewrite the equation in slope-intercept form by solving for y:}
- Slope () = 3
Step 3: Compare the slopes
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A line is parallel to line if it has the same slope, i.e., a slope of 3.
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Option A: Slope = 4 (Not parallel)
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Option B: Slope = 3 (Parallel)
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Option C: Slope = 4 (Not parallel)
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Option D: Slope = 6 (Not parallel)
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Option E: Slope = 3 (Parallel)
Conclusion:
The lines parallel to line are:
- Option B
- Option E
Would you like further details or have any questions?
Here are five related questions to explore:
- How would you determine if two lines are perpendicular instead of parallel?
- What is the relationship between the slopes of perpendicular lines?
- Can two lines be parallel if their slopes are negative reciprocals of each other?
- How does the y-intercept affect the parallelism of two lines?
- What is the significance of the slope-intercept form in graphing linear equations?
Tip: When determining parallelism, always compare the slopes of the lines. Parallel lines will always have identical slopes.
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Math Problem Analysis
Mathematical Concepts
Linear equations
Slope
Parallel lines
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9
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