Math Problem Statement
Find k if the line through (5, 11) and (-3, 7) is parallel to the line through (-2, k) and (2, 5).
Solution
To find , we need to use the fact that the slopes of two parallel lines must be equal.
Step 1: Calculate the slope of the line passing through and .
The slope formula between two points and is given by:
For the points and :
So, the slope of the first line is .
Step 2: Set the slope of the second line equal to the first, since the lines are parallel.
Now, the slope of the line passing through and must also be . Using the slope formula for these points:
Since the slopes must be equal, we set equal to :
Step 3: Solve for .
To solve for , cross-multiply:
Simplify:
Now, solve for :
Final Answer:
The value of is .
Would you like further details or have any questions?
Here are 5 related questions to deepen your understanding:
- How do you find the equation of a line given two points?
- What happens to the slopes of two perpendicular lines?
- How do you find the y-intercept once you have the slope and a point?
- How do you determine if three points lie on the same line?
- What is the geometric interpretation of a slope of zero?
Tip: For any two points, the slope formula is the ratio of the change in y-coordinates to the change in x-coordinates. This gives a precise measure of how steep a line is!
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Math Problem Analysis
Mathematical Concepts
Algebra
Coordinate Geometry
Slopes of Lines
Parallel Lines
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Theorems
Parallel lines have equal slopes
Suitable Grade Level
Grades 8-10
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