You are given two lines in slope-intercept form (y = mx + b) and must find their intersection point. For example, if Line 1 is y = x and Line 2 is y = 3, then the intersect point is (3, 3). Develop a program to find the intersection of any two lines (you can assume there will always be an intersection!). Program Inputs \u2022 Enter m for Line 1: \u2022 Enter b for Line 1: \u2022 Enter m for Line 2: \u2022 Enter b for Line 2: \u2013 You can safely assume the user will always enter real numbers for all questions. Program Outputs \u2022 The intersection point is (XXX,YYY) \u2013 Replace XXX with correct x coordinate and YYY with the y coordinate Sample Output Test Case 1: Enter m for Line 1: 1 Enter b for Line 1: 0 Enter m for Line 2: 0 Enter b for Line 2: 3 The intersection point is (3,3) Test Case 2: Enter m for Line 1: 0.5 Enter b for Line 1: 1 Enter m for Line 2: -2 Enter b for Line 2: 20 The intersection point is (7.6,4.8) Test Case 3: Enter m for Line 1: 3 Enter b for Line 1: -5 Enter m for Line 2: 0.01 Enter b for Line 2: 2 The intersection point is (2.34114,2.02341)<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To determine the intersection point of two lines given in slope-intercept form (y = mx + b), we can follow these steps:<\/p>\n\n\n\n Python Program Implementation<\/strong>:<\/p>\n\n\n\n Explanation<\/strong>:<\/p>\n\n\n\n Sample Outputs<\/strong>:<\/p>\n\n\n\n Note<\/strong>: This program assumes that the lines are not parallel (i.e., m\u2081 \u2260 m\u2082) and will always intersect at a single point. If the lines are parallel, the denominator in the x-coordinate calculation would be zero, leading to a division by zero error.<\/p>\n","protected":false},"excerpt":{"rendered":" You are given two lines in slope-intercept form (y = mx + b) and must find their intersection point. For example, if Line 1 is y = x and Line 2 is y = 3, then the intersect point is (3, 3). Develop a program to find the intersection of any two lines (you can […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-183602","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183602","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=183602"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183602\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183602"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183602"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183602"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
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m\u2081x + b\u2081 = m\u2082x + b\u2082<\/li>\n<\/ul>\n\n\n\n\n
\n
m\u2081x – m\u2082x = b\u2082 – b\u2081<\/li>\n\n\n\n
x(m\u2081 – m\u2082) = b\u2082 – b\u2081<\/li>\n\n\n\n
x = (b\u2082 – b\u2081) \/ (m\u2081 – m\u2082)<\/li>\n<\/ul>\n\n\n\n\n
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y = m\u2081x + b\u2081<\/li>\n<\/ul>\n\n\n\ndef find_intersection(m1, b1, m2, b2):\n # Calculate x-coordinate of intersection\n x = (b2 - b1) \/ (m1 - m2)\n # Calculate y-coordinate of intersection\n y = m1 * x + b1\n return (x, y)\n\n# Input coefficients for Line 1\nm1 = float(input(\"Enter m for Line 1: \"))\nb1 = float(input(\"Enter b for Line 1: \"))\n\n# Input coefficients for Line 2\nm2 = float(input(\"Enter m for Line 2: \"))\nb2 = float(input(\"Enter b for Line 2: \"))\n\n# Find intersection point\nintersection = find_intersection(m1, b1, m2, b2)\n\n# Output the result\nprint(f\"The intersection point is ({intersection[0]:.6f},{intersection[1]:.6f})\")<\/code><\/pre>\n\n\n\n\n
find_intersection<\/code> function computes the x-coordinate of the intersection using the formula:
x = (b\u2082 – b\u2081) \/ (m\u2081 – m\u2082)<\/li>\n\n\n\n
y = m\u2081 * x + b\u2081<\/li>\n\n\n\n\n
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Enter m for Line 1: 1 Enter b for Line 1: 0 Enter m for Line 2: 0 Enter b for Line 2: 3<\/code><\/li>\n\n\n\nThe intersection point is (3.000000,3.000000)<\/code><\/li>\n<\/ul>\n\n\n\n\n
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Enter m for Line 1: 0.5 Enter b for Line 1: 1 Enter m for Line 2: -2 Enter b for Line 2: 20<\/code><\/li>\n\n\n\nThe intersection point is (7.600000,4.800000)<\/code><\/li>\n<\/ul>\n\n\n\n\n
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Enter m for Line 1: 3 Enter b for Line 1: -5 Enter m for Line 2: 0.01 Enter b for Line 2: 2<\/code><\/li>\n\n\n\nThe intersection point is (2.341140,2.023410)<\/code><\/li>\n<\/ul>\n\n\n\n