Math Problem Statement
Solution
The image contains a problem asking to find the equation of a line parallel to the line and passing through the point .
To solve this:
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Identify the slope of the given line , which is the coefficient of . This is .
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Use the point-slope form of the equation of a line, which is:
Where is the slope and is the point through which the line passes. Here, the point is and the slope is .
- Substitute the values into the point-slope form:
Simplifying:
- Distribute the slope:
- Solve for by subtracting 1 from both sides:
Thus, the equation of the line parallel to passing through is:
Would you like further clarification or have any additional questions on this problem? Here are some related questions you can explore:
- How do you find the slope of a line from its equation?
- What is the point-slope form of the equation of a line?
- How do you convert from point-slope form to slope-intercept form?
- How do parallel lines relate to their slopes?
- How do you find the equation of a line passing through a point with a given slope?
Tip: When writing the equation of a line, always check that you use the correct form depending on the information given (e.g., point-slope, slope-intercept).
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Point-Slope Form
Slope-Intercept Form
Formulas
y - y1 = m(x - x1)
Slope-intercept form: y = mx + b
Theorems
Parallel Lines Theorem
Suitable Grade Level
Grades 8-10
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