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Direct Variation

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.

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Direct Variation

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

  2. 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.

  3. Definition • A direct variation can be described by an equation in this form: • The letter k represents the constant of variation. • You say that yvaries directly withx.

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

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

  6. 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?

  7. 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.

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