Section 4.5

Direct Variation

What happens to Y as X goes up by 1?

What happens to Y as X goes up by 1?

Direct Variation

Two variables x and y vary directly if

y = kx

K is a constant number that is not zero. K could be positive or negative.

Direct VariationTwo variables x and y vary directly if

y = kx

Basically, x and y are changing at a constant rate.

As x goes up, y also goes up at a rate of k.

OrAs x goes up, y is going down at a rate of k.

Writing a direct variation equationThe variables x and y varies directly;

When x=5, y=20.

• Y=KX write model for direct variation

• 20=K(5) substitute 5 for x and 20 for y.

• /5 /5 divide each side by 5

• 4=K• So, the equation is y = 4x

• Find the value of y when x=10.• y=4(10) substitute 10 for x and y=4

• Y=40

The variables x and y vary directly. When x=4,y=6 A) write an equation that relates x and yB) find the value of y when x=12.

• SOLUTION• A. Because x and y vary directly, the equation is of the form • y= kx. You can solve for k as follows.• Y= kx write model for direct variation.

• 6= k(4) substitute 4 for x and 6 for y

• 1.5= k divide each side by 4

• Therefore, the equation is y = 1.5 x or y = 3/2 x

Direct variation equation

• An equation that relates X is Y=1.5x

• B) y=1.5(12) substitute 12 for x in y=1.5x Y=18 simplify when X=12, y= 18

The variables x and y vary directly. When x=8,y=3 A) write an equation that relates x and yB) find the value of y when x=12.

Homework

Text Page 238, # 23-31 All