![\"monohybridcross\"](\"https:\/\/schooltutoring.com\/help\/wp-content\/uploads\/sites\/2\/2014\/06\/direct-and-inverse-variation-definitions.png\")
<\/a><\/p>\nDirect Variation<\/h3>\n
Direct variation means that as one variable increases, another variable increases by a specific amount, called a constant. Suppose that when x equals 1, y equals 2; x equals 2, y equals 4; x equals 3, y equals 6; and so on. If x doubles, then y also doubles. \u00a0Another way to describe this relationship is that y varies directly as x. Still another way to describe this relationship in symbol form is that y =2x. Suppose that when a = 1, b = 3; when a = 2, b = 4; when a = 3, b = 6, and so on. In symbol form, b = 3a, and b varies directly as a. In general form, y = kx, and k is called the constant of variation.<\/p>\n
Figure 2: Direct variation has a constant rate of change. As x increases, y increases.<\/p>\n
There are many real-world examples of direct variation. Suppose that a car is traveling at a constant speed of 60 miles per hour. After 1 hour, it travels 60 miles, after 2 hours, it travels 120 miles, and so on. Similarly, suppose that a person makes $10.00 an hour. Their paycheck varies directly with the number of hours they work, so a person working 40 hours will make 400 dollars, working 80 hours will make 800 dollars, and so on. The graph of the values of direct variation will follow a straight line.<\/p>\n Inverse variation means that as one variable increases, the other variable decreases. In equations of inverse variation, the product of the two variables is a constant. Suppose when x equals 3, y equals 20; when x equals 6, y equals 10; and when x equals 12, y equals 5. The relationship in words is that doubling x causes y to halve. The product of x and y, xy, equals 60, so y = 60\/x. Suppose that when x equals 2, y equals \u00bd; when x equals 3; y equals 1\/3; and when x equals 4; y equals \u00bc. The product of xy is 1, and x and y are in a reciprocal relationship. In general symbol form y = k\/x, where k is a positive constant. The constant k is called the constant of proportionality.<\/p>\n Figure 3: In this example of inverse variation, as the speed increases (y), the time it takes to get to a destination (x) decreases.<\/p>\n There are also many real-world examples of inverse variation. Suppose it takes 4 hours for 20 people to do a fixed job. How long will it take 25 people? Time varies inversely as the number of people involved, so if T = k\/n, T is 4, and n is 20, then k will equal 20\u22194, or 80. If n is 25, and k is 80, then T equals 80\/25 or 3.2. Similarly, suppose the current I is 96 amps and the resistance R is 20 ohms. What is the current when R equals 60 ohms? The current varies inversely as the resistance in the conductor, so if I = V\/R, I is 96, and R is 20, then V will equal 96\u221920 or 1920. When V at 1920 is divided by R at 60, then I, the current, is equal to 32 amps.<\/p>\n Figure 4: One of the applications of inverse variation is the relationship between the strength of an electrical current (I) to the resistance of a conductor (R).<\/p>\n Interested in algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/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 Oakdale, CA: visit Tutoring in Oakdale, CA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" Overview Direct and inverse variation refer to relationships between variables, so that when one variable changes the other variable changes by a specified amount. Both direct and inverse variation can be applied in many different ways. Figure 1: Definitions of direct and inverse variation. Direct Variation Direct variation means that as one variable increases, another […]<\/p>\n","protected":false},"author":22,"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":[2655,2656],"class_list":["post-7230","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-direct-variation","tag-inverse-variation"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7230","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=7230"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/7230\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=7230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=7230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=7230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}<\/a><\/p>\nApplications of Direct Variation<\/h3>\n
Inverse Variation<\/h3>\n
<\/a><\/p>\nApplications of Inverse Variation<\/h3>\n
<\/a><\/p>\n