Bellringer

Put your name at the top of the paper

1. Is the set {(2,0), (-1, 9), (4,-2), (3,0), (1,9)} a function?

2. Find the slope of the line that passes through the following points, (9,4) and (3,2).

3. Write in standard form an equation of the line with slope -3 through the point (-2,6).

4. Write y = 7x – 2 in standard form.

5. What is the y-intercept of equation y = 2x +6?

2-3 Direct Variation

M11.A.2.1.2: Solve problems using direct and inverse proportions

M11.D.4.1.1: Match the graph of a given function to its table or equation

Objectives

Writing and Interpreting a Direct Variation

Vocabulary

A linear function defined by an equation of the form

y = kx, where k ≠ 0, represents direct variation.

When x and y are variables, you can write k = , so the ration y : x equals the constant k, the constant of variation.

x

y

Identifying Direct Variation From a Table

For each function, determine whether y varies directly with x.

If so, find the constant of variation and write the equation.

x –1 2 5y 3 –6 15

a.

Since the three ratios are not all equal, y does not vary directly with x.

x 7 9 –4y 14 18 –8

b.

The constant of variation is 2.

The equation is y = 2x.

= and are both equal to –3, but = 3. yx

3–1

–62

155

= 2, so y does vary directly with x.yx

147

189

–8–4= = =

Identifying Direct Variation From an Equation

For each function, tell whether y varies directly with x. If so,

find the constant of variation.

a. 3y = 7x + 7

Since you cannot write the equation in the form y = kx, y does not vary directly with x.

b. 5x = –2y

5x = –2y is equivalent to y = – x, so y varies directly with x.52

The constant of variation is – . 52

The perimeter of a square varies directly as the length of a

side of the square. The formula P = 4s relates the perimeter to the

length of a side.

a. Find the constant of variation.

The equation P = 4s has the form of a direct variation equation with k = 4.

b. Find how long a side of the square must be for the perimeter to be 64 cm.

P = 4s Use the direct variation.

64 = 4s Substitute 64 for P.

16 = s Solve for s.

The sides of the square must have length 16 cm.

Real World Example

Suppose y varies directly with x, and y = 15 when x = 27.

Find y when x = 18. Let (x1, y1) = (27, 15) and let (x2, y2) = (18, y).

15(18) = 27(y) Write the cross products.

y = 10 Simplify.

Write a proportion.y1

x1

y2

x2

=

Substitute.=1527

y18

y = Solve for y.15 • 18

27

Using Proportion

Homework

Pg 74 & 75 #1,2,9,10,17,18,23,24,25