Math Problem Statement
Solution
The image presents two perpendicular lines, and the task is to find the slope-intercept form of the equation of line , based on the equation given for line . The equation of is:
Key Information:
- The lines are perpendicular, meaning the product of their slopes must equal .
- The slope of is (since the equation is in the form , where is the slope).
- For perpendicular lines, if the slope of one line is , the slope of the other line is .
Thus, for line , the slope is:
The equation of line is also in the form . Now, to find the y-intercept , we can use the point where the two lines intersect, which is given as . Using this point in the equation :
Thus, the equation of is:
Let me know if you would like further clarification or additional details.
Related Questions:
- How do you find the equation of a line if the slope and a point on the line are given?
- What is the significance of perpendicular lines in terms of their slopes?
- How can you verify the intersection point of two lines algebraically?
- What method would you use to find the distance between two lines?
- How do parallel and perpendicular slopes differ in geometry?
Tip:
Always remember, for two lines to be perpendicular, their slopes must multiply to . This relationship helps in quickly identifying the slope of the perpendicular line.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Perpendicular Lines
Formulas
Slope-intercept form: y = mx + b
Perpendicular slope: m1 * m2 = -1
Theorems
Slopes of perpendicular lines theorem
Suitable Grade Level
Grades 8-10
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