Warm Up #4.

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Section 3 Direct Variation

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Presentation transcript:

Warm Up #4

HW Check – Inverse Worksheet

2.3 - Direct Variation

Direct Variation A linear function defined by an equation of the form y = kx, where k ≠ 0, represents direct variation.

Constant of Variation The Slope, k, is constant. It can be represented at the ratio of

Identifying Direct Variation from a Table Determine whether y varies directly with x. If so, find the constant of variation and write the equations. 1. 2. X Y 2 8 3 12 5 20 X Y 1 4 2 7 5 16

You Try!! Determine whether y varies directly with x. If so, find the constant of variation and write the equations. 1. 2. X Y -1 -2 3 4 6 7 X Y -6 -2 3 1 12 4

Identifying Direct Variation from an Equation For each function, determine whether y varies directly with x. If so, find the constant of variation: y = 4x 2y = 3x y = 2x + 3

You Try!! Determine whether y varies directly with x. If so, find the constant of variation. y = x/2 2y – 1 = x 4x = 8y 7x + 4y = 10

Using Proportions If we know that y varies directly with x. We can use proportions to find missing information. Ex. Suppose y varies directly with x, and x = 3 when y = 7. Find x when y = 21.

You Try! y varies directly with x: If y = 25 when x = 15, find x when y = 10 If y = 30 when x = -3, find y when x = -9

Writing Equations Write an equation of the direct variation that includes the point (10, -15). You Try: Write an equation of the direct variation that includes the point (-40, 16).

Word Problems The Height of an object varies directly with the length of its shadow. A person 6 ft tall casts an 8.5 ft shadow, while a tree casts a 38 ft shadow. How tall is the tree?

Word Problem The amount of a persons paycheck p varies directly with the numbers of hours worked t. For 4o hours of work, the paycheck is $390. Write an equation for the relationship between hours worked and pay.

Direct Variation Worksheet Turn in when you are done! Class work – Group Work Direct Variation Worksheet Turn in when you are done!

Mid-Chapter Review Sheet # 4 – 15 Show all work for credit!! Homework Mid-Chapter Review Sheet # 4 – 15 Show all work for credit!!