Math Problem Statement
parallel to 5x+6y=-1 and passes through (3,2)
Solution
To find the equation of the line parallel to and passing through the point , we need to follow these steps:
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Find the slope of the given line:
The equation of the line is in standard form: .
To find the slope, we first rewrite the equation in slope-intercept form, , where is the slope.The slope of this line is .
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Use the point-slope form:
Since parallel lines have the same slope, the slope of the new line is also .
Now, use the point-slope form of a line equation:where is the given point and .
Substituting the values:
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Simplify the equation: Distribute the slope on the right-hand side:
Now, add 2 to both sides:
Thus, the equation of the line parallel to and passing through is:
Would you like more details on any step, or do you have any questions?
Here are 5 related questions to explore this concept further:
- How do you convert from point-slope form to standard form?
- What is the difference between parallel and perpendicular lines in terms of slope?
- Can you find the equation of a line perpendicular to ?
- What happens if a line passes through the origin?
- How do you find the distance between two parallel lines?
Tip: Parallel lines always have the same slope but different intercepts!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Parallel Lines
Slope-Intercept Form
Point-Slope Form
Formulas
Slope-intercept form: y = mx + b
Point-slope form: y - y1 = m(x - x1)
Theorems
Parallel lines have the same slope
Suitable Grade Level
Grades 9-11
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