Two lines are said to be parallel if the angle between them is zero. There is a result on parallel line which is states as : “Two lines are parallel if and only if their slopes are equal.”<\/p>\n
i.e. If the slopes <\/a>of two lines which are parallel are m1<\/strong> and m2<\/strong> then m1<\/strong> = m2<\/strong>.<\/p>\n Example:<\/span><\/strong><\/p>\n The slope of a line is 3\/2<\/strong>. If a line is parallel to this line, what is the slope of this new line?<\/p>\n Solution:<\/span><\/strong><\/em><\/p>\n By the condition for the slopes of parallel lines,<\/p>\n m1=m2.<\/strong><\/p>\n So, the slope of new line = 3\/2.<\/strong><\/p>\n For finding the equation of a line parallel to ax+by+c=0<\/strong> and passing through the point (x1,y1), there are 2 methods.<\/p>\n (1)\u00a0\u00a0\u00a0 Finding the slope of ax+by+c=0<\/strong> which can be obtained by the expression \u2013a\/b<\/strong>.<\/p>\n i.e. slope of ax+by+c=0<\/strong> is m=-a\/b<\/strong>.<\/p>\n (2)\u00a0 Then the corresponding equation of parallel line can be found using point slope form.<\/p>\n i.e., the required equation is,<\/p>\n y-y1=m(x-x1)<\/strong><\/p>\n Example:<\/span><\/strong><\/p>\n Find the equation of line parallel to 3x+y+3=0<\/strong> and passing through (-1,2<\/strong>).<\/p>\n Solution:<\/span><\/strong><\/em><\/p>\n The slope of given line, m = -3\/1=-3<\/strong><\/p>\n (x1,y1) = (-1,2).<\/strong><\/p>\n The equation of parallel line is,<\/p>\n y-y1=m(x-x1)<\/strong><\/p>\n y-2 = -3 (x+1)<\/strong><\/p>\n y-2 = -3x-3<\/strong><\/p>\n 3x+y+1=0.<\/strong><\/p>\n (1)\u00a0\u00a0\u00a0 Take the equation of line parallel to ax+by+c=0<\/strong> as ax+by+k=0<\/strong> where k<\/strong> is a constant.<\/p>\n (2)\u00a0\u00a0\u00a0 The value of \u2018k<\/strong>\u2019 can be found by substituting the given point (x1,y1<\/strong>) in the equation ax+by+k=0.<\/strong><\/p>\n (3)\u00a0\u00a0\u00a0 Substitute \u2018k<\/strong>\u2019 back into the equation ax+by+k=0<\/strong> which is the required equation.<\/p>\n Example:<\/span><\/strong><\/p>\n Find the equation of line parallel to 3x+y+3=0<\/strong> and passing through (-1,2<\/strong>).<\/p>\n Solution:<\/span><\/strong><\/em><\/p>\n The equation of line parallel to 3x+y+3=0<\/strong> is,<\/p>\n 3x+y+k=0.<\/strong><\/p>\n Here x=-1<\/strong> and y=2<\/strong><\/p>\n 3(-1)+2+k=0<\/strong><\/p>\n k-1=0<\/strong><\/p>\n k=1<\/strong><\/p>\n So the required equation of parallel line is,<\/p>\n 3x+y+1=0.<\/strong><\/p>\n SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Hollister visit: Tutoring in Hollister.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" Two lines are said to be parallel if the angle between them is zero. There is a result on parallel line which is states as : “Two lines are parallel if and only if their slopes are equal.” i.e. If the slopes of two lines which are parallel are m1 and m2 then m1 = […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[584,588,1280,1660],"class_list":["post-2587","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-equal","tag-equation","tag-parallel","tag-slope"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2587","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=2587"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2587\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=2587"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=2587"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=2587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Finding the Equation of Parallel Lines:<\/h3>\n
Method 1:<\/h4>\n
Method 2:<\/h4>\n