2.6 – Direct Variation

A simplified form of the equation y = mx + b could be an equation with a y-intercept of 0 Direct Variation = as one variable changes, the other changes at a constant rate y = kx k = constant of variation What else could k represent?

Properties; 1) y intercept of 0 2) If k > 0, then treat as a positive slope 3) If k < 0, then treat as a negative slope

Graphing To graph a direct variation equation, same as graphing in slope-intercept form If b = 0, then where would we start? Example. Graph y = 4x.

Example. Graph y = (-2/3)x

Determining Direct Variation An equation is considered direct variation if and only the change is constant If the change is not constant, you would get non-linear graphs

Example. Tell whether the following represents direct variation.

Finding Constant of Variation Typically with direct variation, we will not know 2 points – Issue is, from before, how many points do we need for the slope? Luckily, we can get around that with direct variation If two variables vary directly, then we will only need to solve for the missing k value

Example. x and y vary directly. Write an equation that relates x and y, and find y when x = 9. Assume x = 3 when y = 27.

Example. x and y vary directly. Write an equation that relates x and y, and find y when x = 9. Assume x = -2 when y = -12.

Applications What occasions can you think of when you change one item (variable), and it directly will alter or change another? One example is gravity. Different planets have different gravitational pulls.

Example. On Earth, Coach Jones weighs in at a sprightly 160 pounds. If he were to travel to the moon, he would weigh in at 26.5 pounds. If an item weights 200 pounds, how much could it weigh on the moon? Write an equation to show direct variation of gravity and your earth weight.

Example. The sales tax t on an item varies directly with the price p. In Florida, the state sales tax is 6%. Write an equation for that relates t and p, and find how much sales tax you would pay on an item costing $260.

Assignment Pg , odd, even, 37, 40, 44, 65