Math Problem Statement
Solution
We are tasked with finding the equation of line , which is perpendicular to line and passes through the point .
Step 1: Find the slope of line
The equation of line is: We need to rewrite this in slope-intercept form to find the slope.
Rearranging the terms: So, the slope of line is .
Step 2: Find the slope of line
Since line is perpendicular to line , the slope of line , , will be the negative reciprocal of . The negative reciprocal of is .
Step 3: Use the point-slope form to find the equation of line
Now that we have the slope and a point that lies on line , we use the point-slope form: Substitute , , and : Simplifying: Convert 9 to a fraction with a denominator of 3:
Final Answer:
The equation of line in slope-intercept form is:
Would you like any further details or explanations?
Here are 5 related questions to expand on this:
- How do you find the equation of a line parallel to a given line?
- What is the geometric significance of the slope being the negative reciprocal?
- How do you convert between different forms of a line equation (standard, point-slope, slope-intercept)?
- How can you determine if two lines are perpendicular using only their equations?
- Can you find the equation of a line parallel to line that passes through a different point?
Tip: When dealing with perpendicular lines, remember that their slopes are always negative reciprocals of each other.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Algebra
Coordinate Geometry
Formulas
Slope-intercept form: y = mx + b
Point-slope form: y - y1 = m(x - x1)
Theorems
Perpendicular lines have slopes that are negative reciprocals
Suitable Grade Level
High School
Related Recommendation
How to Find the Equation of a Line Perpendicular to Another and Passing Through a Point
Finding Equations of Perpendicular Lines through Specific Points
Finding the Equation of a Perpendicular Line through a Given Point
Equation of Perpendicular Line through Point (-2, 2)
Finding the Equation of a Line Perpendicular to Another Line