Section 4.5 Direct Variation. What happens to Y as X goes up by 1?

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Presentation transcript:

Section 4.5 Direct Variation

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 Variation Two 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. Or As x goes up, y is going down at a rate of k.

Writing a direct variation equation The 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 y B) 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 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 y B) find the value of y when x=12.

Homework Text Page 238, # All