Math Problem Statement
Solution
Let's break down this problem:
Given:
- Line passes through the points and .
- The point is at , and we need to find another point on a line parallel to that passes through , and has integer coordinates.
Step 1: Find the slope of line
The slope of a line passing through two points and is given by: For the points and , the slope of line is:
Step 2: Find the equation of the line parallel to and passing through
A line parallel to will have the same slope, . The equation of a line with slope passing through point is: Substituting , , and , we get: Simplifying:
Step 3: Find a point with integer coordinates
To find integer coordinates, we substitute the given answer choices into the equation of the parallel line:
-
For : Not an integer.
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For : This works since .
Thus, the point lies on the line parallel to and passes through .
Final Answer:
The correct point is .
Would you like further details, or do you have any questions?
Here are 5 related questions to consider:
- How would you find the equation of the line in slope-intercept form?
- What is the significance of finding the slope of a line for parallel lines?
- How can we determine if two lines are perpendicular based on their slopes?
- What is the general form of the equation of a line, and how is it derived from the slope-intercept form?
- How could you check if a point lies on a given line using its equation?
Tip: Parallel lines always have the same slope but different y-intercepts!
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Algebra
Parallel Lines
Formulas
Slope Formula: m = (y2 - y1) / (x2 - x1)
Point-Slope Form: y - y1 = m(x - x1)
Theorems
Concept of Parallel Lines
Suitable Grade Level
Grades 8-10
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