📚 Topic Summary
Perpendicular lines are lines that intersect at a right angle (90 degrees). The slopes of perpendicular lines have a special relationship: they are negative reciprocals of each other. If one line has a slope of $m$, then a line perpendicular to it will have a slope of $-\frac{1}{m}$. This worksheet will guide you through understanding and applying this concept to write equations of perpendicular lines.
🧮 Part A: Vocabulary
Match each term with its definition:
- Term: Slope
- Term: Y-intercept
- Term: Perpendicular Lines
- Term: Negative Reciprocal
- Term: Linear Equation
- Definition: Lines that intersect at a 90-degree angle.
- Definition: A mathematical statement showing the equality of two expressions, resulting in a straight line when graphed.
- Definition: The point where a line crosses the y-axis.
- Definition: A number that, when multiplied by another number, equals -1.
- Definition: A measure of the steepness of a line.
Match the terms above. For example, if you think 'Slope' matches with 'Lines that intersect at a 90-degree angle', write 1-A.
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided:
Words: slope, negative reciprocal, y-intercept, perpendicular, equation
Two lines are considered _________ if they intersect at a right angle. The relationship between their _________ is that they are _________ of each other. To write the _________ of a line, you also need to know its _________.
🤔 Part C: Critical Thinking
Explain in your own words why the slopes of perpendicular lines are negative reciprocals of each other. How does this relationship ensure the lines intersect at a 90-degree angle?