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5 – 4 A: Direct Variation Homework Review A line has a slope of 5 and passes through the points (4,3) and (2,y). What is the value of y? y = -7 Homework Review A line passes through the origin and has a slope of . Through which quadrants does the line pass? II and IV Definitions Direct variation – linear relationship between two variables that can be written in the form y = kx Constant of variation – the fixed number (k) in a direct variation (the coefficient) **This is another expression that means slope or rate of change.*** Direct Variation • Will be a straight line when graphed • ALWAYS passes through the origin (0,0) Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = 2x Yes k=2 Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = 1/3 x Yes k = 1/3 Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = - ½x Yes k = -½ Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = 2x + 3 No Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = ½x - 6 No Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. 2y = x Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. 2y = x 2 2 y=½x Yes, this is a direct variation. ½ is the constant of variation. Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y + 1 = 2x . Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y + 1 = 2x Solve for y. -1 -1 . y = 2x – 1 . This is not in the form y = kx, so this is not a direct variation. Work with your partner. Page 214 (1-4) Notes: The graph of a direct variation is a line that passes through the origin (0 0). The constant of variation (k) is the slope of the line. Does this graph represent a direct variation? • Yes, the line passes through the origin, so this is a direct variation. • What is the slope of the line (constant of variation)? k=1 Does this graph represent a direct variation? • Yes, the line passes through the origin, so this is a direct variation. • What is the constant of variation? k = -½ Does this graph represent a direct variation? • No, the line does not pass through the origin, so this is NOT a direct variation. Does this graph represent a direct variation? • No, the line does not pass through the origin, so this is NOT a direct variation. Does this graph represent a direct variation? • Yes, the line passes through the origin, so this is a direct variation. 22 20 18 16 14 12 • What is the constant of variation? k=2 10 8 6 4 2 y = 2x 0 0 1 2 3 4 5 6 7 8 9 10 Does this graph represent a direct variation? • No, this is not a straight line, so this is NOT a direct variation. Let’ look at: Page 214 (7-8) Partner Talk Page 215 (19-24) Homework: Page 214 (10-13, 16-17)