Math Problem Statement
Solution
We are asked to find the equation of a line that passes through the point and is parallel to the line given by .
Step 1: Determine the slope of the given line
We can first find the slope of the line by rewriting it in slope-intercept form, , where is the slope.
Solve for :
From this equation, we can see that the slope of the given line is .
Step 2: Use the slope-point form
Since the line we need to find is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also .
Now, using the point-slope form of a line equation:
Where , . Substituting these values:
Step 3: Simplify the equation
Final Answer:
The equation of the line passing through and parallel to is:
Would you like further details or clarification?
Related Questions:
- How do you find the slope of a line from its equation?
- What is the general form of the point-slope equation of a line?
- How can you verify if two lines are parallel?
- How do you convert a linear equation from standard form to slope-intercept form?
- Can a line parallel to another line ever intersect it?
Tip:
When two lines are parallel, their slopes are always equal! Use this to your advantage when writing the equation of a line.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
Slope-intercept form y = mx + b
Point-slope form y - y1 = m(x - x1)
Theorems
Parallel Lines Theorem
Suitable Grade Level
Grades 8-10
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