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Model Direct Variation (4.6) Definition: Direct Variation is a linear function that can be written in the form y = kx (where x ≠ 0) Definition: k is called the constant of variation **Think of the y = mx + b form. ** y = kx means that m = ______ and b = ______ So all direct variations will go through the _______________________ Is the equation a direct variation? If it is, find the constant of variation (k). ** To determine if an equation is a direct variation, solve the equation for y. Ex. 5x + 2y = 0 Ex. 4y = 3x + 12 Graph the direct variation equation. (Graph like slope-intercept form, where k = m and b = 0) Ex. 2x + y = 0 Ex. 6y = 10x 1 Solve y = kx, for k To Write a Direct Variation Given one value for x and y Step 1—Find k (Use the equation above) Step 2—Write the equation y = kx and substitute your k value Given that y varies directly with x, use the specified values to write a direct variation equation that relates x and y Ex. x = 2, y = -8 Ex. x = 40, y = 15 Ex. The size of a file (s) varies directly with the amount of time (t) download a file. It takes 15 seconds to download a 420kb file. a) Write a direct variation that relates s and t b) How much time will it take to download a file that is 1260kb? 2