Math Problem Statement
Solution
Let’s solve the two parts of the question.
Part A:
The equation of line is given as .
Another line is perpendicular to and passes through the point .
Step 1: Determine the slope of line .
The slope of line is . For perpendicular lines, the slopes are negative reciprocals.
Thus, the slope of line is:
Step 2: Find the equation of line .
The slope-intercept form of a line is:
Here , and the line passes through . Substitute , , and into the equation to solve for :
Thus, the equation of line is:
The correct answer is C.
Part B:
We are told that line has a slope of . Another line is parallel to .
Key Concept: Parallel lines have the same slope.
Thus, the slope of line is:
Final Answers:
- Part A: The equation of line is (Answer C).
- Part B: The slope of line is .
Would you like me to go into further detail about any of the steps? Here are some related questions:
- How do you find the slope of a perpendicular line?
- What is the significance of the y-intercept in a line equation?
- How are parallel and perpendicular lines related in geometry?
- Could you explain more about the negative reciprocal rule for slopes?
- What happens if the line does not pass through a given point?
Tip: Always verify whether a line equation satisfies the given conditions by substituting the point into the equation.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Equations
Slopes of Perpendicular Lines
Slopes of Parallel Lines
Formulas
Slope-intercept form: y = mx + b
Perpendicular slope relation: m1 * m2 = -1
Theorems
Slope of perpendicular lines
Slope of parallel lines
Suitable Grade Level
Grades 8-10