Direct Variation The graph of a direct variation is always a line that passes through the origin.

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Presentation transcript:

Direct Variation The graph of a direct variation is always a line that passes through the origin.

Direct Variation When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation.

Definition A direct variation can be described by an equation in this form: The letter k represents the constant of variation. You say that y varies directly with x.

If y varies directly as x and y = 8 when x = 12, find k and write an equation that expresses this variation.

If y varies directly as x and y = 24 when x = 16, find y when x = 12.

To Do….in groups of 3/4 In both inches and centimeters, find the length of  One shoe in your group.  The smallest assignment book in your group.  The youngest person’s index finger.  The oldest person’s wrist.  The other person’s wrist to elbow. Make a scatter plot of these data. Decide as a class which unit to put on the x -axis. Find a line of fit. Identify and interpret the meaning of the slope. Identify and interpret the meaning of the y -intercept. Is this a direct variation?

To Do….in groups of 3 Using a CBR, walk for 5 seconds to create a line that has a positive slope.  Record the time and distance for seconds 0, 1, 2, 3, 4, 5.  Find a line of fit.  Identify and interpret the meaning of the slope.  Identify and interpret the meaning of the y-intercept.  Is this a direct variation? Repeat for a line that has a negative slope. Repeat for a line that has a zero slope.