Perpendicular lines are lines that intersect at a right angle (90 degrees). A key property of perpendicular lines, crucial for writing their equations, is that their slopes are negative reciprocals of each other. If one line has a slope of $m$, a line perpendicular to it will have a slope of $-\frac{1}{m}$. This relationship allows us to determine the equation of a perpendicular line if we know the equation of the original line and a point it passes through.
To find the equation of a perpendicular line, first determine the slope of the given line. Then, find the negative reciprocal of that slope. Finally, use the point-slope form of a linear equation, $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the new line and $m$ is the new slope, to write the equation. Convert to slope-intercept form ($y = mx + b$) if needed.
| Term | Definition |
|---|---|
| 1. Slope | A. A line that intersects another line at a 90-degree angle. |
| 2. Y-intercept | B. The point where a line crosses the y-axis. |
| 3. Perpendicular Lines | C. The measure of the steepness of a line. |
| 4. Negative Reciprocal | D. The form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. |
| 5. Slope-Intercept Form | E. The result of flipping a fraction and changing its sign. |
Match the term to its definition.
Perpendicular lines intersect at a ______ angle. The slopes of perpendicular lines are ______ reciprocals of each other. If a line has a slope of 2, a line perpendicular to it has a slope of ______. To write the equation of a perpendicular line, you need to know the slope of the original line and a ______ on the new line. The point-slope form of a line is given by the equation ______.
Explain in your own words how to find the equation of a line that is perpendicular to $y = 3x + 2$ and passes through the point (1, 5).
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