3-5 Proportional and Nonproportional Relationships Inductive Reasoning: Using a pattern to find a general rule. Find the next 3 terms of the sequences. -3, -1, 3, 9, ____, ____, ____ 18, 21, 25, 30, ____, ____, ____ 17 27 39 36 43 51

Finding Equations from Relations 13 15 5, 7, 9, 11, ____, ____ -1, -4, -7, -10, ____, ____ -13 -16 x 1 2 3 4 5 6 y 8 12 ___ 16 20 24 This suggests y = 4x

Write an equation for this… If it goes through the origin (0,0) you do not add or subtract a constant number at the end of the equation. You just need to figure out what comes before the x. Look at the relationship between x and y. When x is 1, what is y? When x is 2, what is y? When x is -1, what is y? When x is -2, what is y? Do you see a pattern? Equation is y = 2x Called Proportional when the graph passes through the origin (0,0)

Try this one… What is the relationship between x and y? y = -3x

When the line doesn’t go through the origin…it is called Nonproportional When the graph is moved up or down, you need to add or subtract that number at the end of the equation. It crosses the y axis at -2 so you need to subtract 2 from the end of the equation. Now look at the relationship between x and y… x -2 -1 1 2 3 y As x goes up by one, y goes up by 2 so… -6 -4 -2 2 4 y = 2x - 2

Try This One… y = 3x + 2