For example, if y represents the total cost of buying x items that cost $7 each, then the direct variation equation would be. y = 7x. in this direct variation equation, 7 is the constant of proportionality, which represents the cost per item. and, for example: when x=2, y=14. when x=3, y=21. when x=10, y=70. Y = 48. therefore, 8 dozen oranges will cost $48. now, let us find the constant of direct variation by using the equation y = kx. where. y = the cost, x = the number of dozens, and. k = the constant of variation. k = 1 6. therefore, 1 6 or 0.1667 (approx) is the constant of direct variation.
A direct variation equation is a mathematical relationship between two variables where the ratio of the two remains constant. in other words, when one variable increases, the other increases proportionally, and vice versa. this relationship is often expressed in the form y = kx, where y and x are the two variables, and k is the constant of. Real life examples of direct variation. below are two examples illustrating the concept of direct variation: example `1`: let's consider the relationship between the time taken to travel a certain distance and the speed of travel. when driving at a constant speed, the time it takes to travel a certain distance directly varies with the speed. The sign “ ∝ ” is read “varies as” and is called the sign of variation. example: if y varies directly as x and given y = 9 when x = 5, find: a) the equation connecting x and y. b) the value of y when x = 15. c) the value of x when y = 6. solution: a) y ∝ x i.e. y = kx where k is a constant. substitute x = 5 and y = 9 into the equation:. Guidelines for solving a direct variation equation. write a general formula for direct variation that involves the variables and a constant of variation. write the direct variation formula in the form y = kx, where k ≠ 0. find the value of k in guideline 1 by using the initial data given in the statement of the problem.
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