Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Coordinate Geometry
Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …
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**2. The Line Parallel to a Given Line** Find the equation of the line parallel to \( y = \frac{2}{3}x + 5 \) that passes through the point \( (3, 2) \). To determine the equation of a line that is parallel to the given line \( y = \frac{2}{3}x + 5 \), we note that parallel lines have the same slope. Therefore, the slope of the line we are seeking is also \( \frac{2}{3} \). Using the point-slope form of a line equation \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point through which the line passes, we substitute the known values: - \( m = \frac{2}{3} \) - \( (x_1, y_1) = (3, 2) \) This results in: \[ y - 2 = \frac{2}{3}(x - 3) \] Simplifying this gives the equation of the desired line in slope-intercept form: \[ y = \frac{2}{3}x - \frac{2}{3} \]
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Transcribed Image Text:**2. The Line Parallel to a Given Line** Find the equation of the line parallel to \( y = \frac{2}{3}x + 5 \) that passes through the point \( (3, 2) \). To determine the equation of a line that is parallel to the given line \( y = \frac{2}{3}x + 5 \), we note that parallel lines have the same slope. Therefore, the slope of the line we are seeking is also \( \frac{2}{3} \). Using the point-slope form of a line equation \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point through which the line passes, we substitute the known values: - \( m = \frac{2}{3} \) - \( (x_1, y_1) = (3, 2) \) This results in: \[ y - 2 = \frac{2}{3}(x - 3) \] Simplifying this gives the equation of the desired line in slope-intercept form: \[ y = \frac{2}{3}x - \frac{2}{3} \]
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