Examples, solutions, videos, and worksheets to help grade 7 students learn how to find the equation of a line passing through a given point and perpendicular to a given line.
How to find the equation of Perpendicular Lines?
There are three sets of Perpendicular Lines worksheets:
- Equation given in slope-intercept form
- Equation given in standard form
- Equation in both forms
To find the equation of a line that is perpendicular to a given line, you need the slope of the given line and the point at which the perpendicular line should pass. Perpendicular lines have negative reciprocal slopes, so if you know the slope of the given line, you can use it to find the slope of the perpendicular line.
Here are the steps to find the equation of a perpendicular line:
- Determine the slope of the given line. The slope (m) can be found by rearranging the equation into the slope-intercept form (y = mx + b) and identifying the coefficient of x (m).
- Find the negative reciprocal of the slope (m) to get the slope of the perpendicular line. The negative reciprocal is -1/m.
- To find the specific equation of the perpendicular line, you need a point through which it passes. If you have a point (x1, y1) that the perpendicular line must pass through, substitute these coordinates into the equation: y = -1/m x + c
- Solve for c to find the specific equation of the perpendicular line.
Example:
Find the equation of a line perpendicular to y = 3x + 2 that passes through the point (4, 5).
- Start with the given line: y = 3x + 2.
- The negative reciprocal of 3 is -1/3
- Substitute the point (4, 5) into the equation: 5 = -1/3 (4) + c.
- Solve for c: c = 5 + 4/3 = 6 1/3 = 19/3
The equation of the perpendicular line is: y = -1/3 x + 19/3.
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