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Linear Models and Direct Variation Equations

Learn to write equations of lines and linear models based on given data points, slopes, and constant variations. Use predictive models and graphing techniques for analysis.

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Linear Models and Direct Variation Equations

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  1. 2.4 – Writing Equations of Lines

  2. Models of Lines

  3. Write an equation of a line. 1. Passes through (-3, 4) and has a slope of 2/3

  4. Write an equation of a line. 2. Passes through (5, 2) and has a slope of -3

  5. Write an equation of a line. 3. Passes through (1, 5) and (4, 2)

  6. Write an equation of a line. 4. Passes through (3, 0) and (-3, 1)

  7. In 1984, American’s purchased an average of 113 meals per person at restaurants. By 1996, it was 131. Write a linear model and use it to predict the number of meals purchased in 2010.

  8. In 1991, 57 million cats were pets in the US. By 1998, there were 61 million. Write a linear model then use it to predict the number of cats that are pets in 2009.

  9. Direct Variation • When two variables are related in such a way that the ratio of their values remains constant. • “y varies directly as x” would simply mean as x increases – so does y. Or as x decreases – so does y. • Form: y = kx, k = constant of variation.

  10. The variable x and y vary directly and y=15 when x=3. a) Write and graph the equation relating x and y.b) Find y when x = 9.

  11. The variable x and y vary directly and y=19.22 when x=6.2. a) Write and graph the equation relating x and y.b) Find y when x = 4.3.

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