Math Problem Statement
Solution
We are asked to write the equation of a line passing through the point and parallel to the line given by the equation .
Step 1: Identify the slope
The line is in slope-intercept form , where is the slope. From the equation, the slope .
Since the new line is parallel to the given line, it will have the same slope, i.e., .
Step 2: Use the point-slope form
The point-slope form of a line is: where is the point the line passes through and is the slope. Substituting for and for , we get: Simplifying:
Step 3: Distribute the slope
Now distribute the on the right-hand side:
Step 4: Solve for
Subtract 4 from both sides to get the equation in slope-intercept form:
Thus, the equation of the line passing through the point and parallel to is:
Would you like further details or have any questions about this solution?
Related questions:
- How would the equation change if the line were perpendicular instead of parallel?
- What is the y-intercept of the new line?
- Can you explain how to convert a line equation from point-slope form to slope-intercept form?
- What is the general form of a linear equation?
- How do we determine the equation of a line passing through two given points?
Tip:
When finding equations of parallel lines, remember that they always share the same slope but have different y-intercepts unless they are the same line.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Point-Slope Form
Slope-Intercept Form
Formulas
Slope-Intercept Form: y = mx + b
Point-Slope Form: y - y1 = m(x - x1)
Theorems
Parallel Line Theorem: Parallel lines share the same slope
Suitable Grade Level
Grades 9-10
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