Math Problem Statement
Are the lines 2y+x=4 and y+x+8=0 parallel
Solution
To determine if the lines and are parallel, we need to find their slopes. Parallel lines have the same slope.
Step 1: Rewrite each equation in slope-intercept form , where is the slope.
For the first equation :
-
Subtract from both sides:
-
Divide by 2 to solve for : The slope of the first line is .
For the second equation :
- Subtract from both sides: The slope of the second line is .
Step 2: Compare the slopes
- The slope of the first line is .
- The slope of the second line is .
Since , the lines are not parallel.
Would you like more details on how to determine slopes or solve linear equations? Here are some related questions you might find useful:
- What are the conditions for two lines to be perpendicular?
- How do you find the point of intersection between two lines?
- Can two lines have the same slope but not be parallel?
- What is the general equation of a line in 3D space?
- How can you check if a set of lines is concurrent?
Tip: When comparing the slopes of two lines, remember that parallel lines will always have identical slopes, while perpendicular lines have slopes that are negative reciprocals of each other.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slopes
Formulas
Slope-intercept form y = mx + b
Slope comparison for parallel lines
Theorems
Parallel Line Theorem
Suitable Grade Level
Grades 8-10
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