College Math

The

slope of two parallel lines is always the same. In other words, two lines are parallel only when they have the same slope. In contrast, the slope of perpendicular lines is opposite reciprocals. For instance, if the slope of one line is 2, then the line parallel to this line would also have the slope of 2, while the line perpendicular to this line would have the slope equal to -1/2. Just to revise the concept (studied in first chapter), the slope of the line can be found by finding the x-intercept of the equation of the line, where line is represented by y = ax + b. In this equation, ‘a’ is the slope. For instance, let us consider the following two pair of lines: Cas I: y – 3x = 5 and y -3x = -5 In this case, y = 3x + 5 and y = 3x – 5 The slope for both the lines is 3, hence are parallel to each other. Case II: 7x – 3y = 5 and 7y + 3x = 6 In this case, y = 7/3x -5/3 and y = -3x/7 + 6/7 The slope for first line is 7/3 while that of the other is -3/7, which are opposite reciprocals to each other, and hence, are perpendicular. Sometimes, we may need to find the equation of a line parallel to given line, when the intercepts of the same are given. For instance, how do we find the equation of a line with intercepts (3, 2), which is parallel to 3x + y = -3 In this case, we know that the desired line will have the same slope as for the given line. So we find the slope of the given line. 3x + y = -3 y = –3x – 3 Slope of the line is -3. Now, in order to find the equation of the line parallel to the above given line, substitute the intercepts and slope in the line equation, that is: (y – y 1 ) = m (x – x 1 )

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