Direct Variation Equations

ReviewWhat is the slope?

Slope = 1/2

Slope = -1

Slope = 5

Slope = Undefined

65 mph

1. What was the greatest speed that Michael traveled?

Constant Speed

2. What does the horizontal segment of the graph represent? How long does Michael stay at this speed?

70 mins - 20 mins = 50 mins

Speed is decreasing

3. What does the segment with a negative slope tell you about Michael’s speed?

Speed is increasing

4. What does the segment with a positive slope tell you about Michael’s speed?

Vocabulary

• Direct Variation Equation – An equation of the form y = kx, where k does not equal zero

• Constant of Variation – k in a direct variation equation

Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points.

Slope formula

Simplify.

Answer: The constant of variation is 2. The slope is 2.

Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points.

Slope formula

Simplify.

Answer: The constant of variation is –4. The slope is –4.

Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

a. Answer: constant ofvariation: 4; slope: 4

Answer: constant ofvariation: –3; slope: –3

Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

b.

• The constant of variation is the slope

Find the value of k.Direct variation formula

15 = k(5) Replace y with 15 and x with 5.

15 = k(5) 5 5 Divide each side by 5

3 = k Simplify

Equation?

y = 3x

Y varies directly as x. Find the constant of variation and write an equation for the direct variation.5. Y = 15 when x = 5

Find the value of k.Direct variation formula

9 = k(3) Replace y with 15 and x with 5.

9= k(3)3 3 Divide each side by 5

3 = k Simplify

Equation?

y = 3x

Y varies directly as x. Find the constant of variation and write an equation for the direct variation.7. Y = 9 when x = 3

Find the value of k.Direct variation formula

18 = k(11) Replace y with 15 and x with 5.

18= k(11)11 11 Divide each side by 518 = k Simplify11

Equation?

y = 18x 11

Y varies directly as x. Find the constant of variation and write an equation for the direct variation.9. y = 18 when x = 11

Find the value of k.Direct variation formula

42 = k(7) Replace y with 15 and x with 5.

42= k(7) 7 7 Divide each side by 56 = k Simplify

Equation?

y = 6x

Y varies directly as x. Find the constant of variation and write an equation for the direct variation.11. y = 42 when x = 7

Find the value of k.Direct variation formula

12 = k(22) Replace y with 15 and x with 5.

12= k(22)22 22 Divide each side by 56 = k Simplify11

Equation?

y = 6 x 11

Y varies directly as x. Find the constant of variation and write an equation for the direct variation.13. y = 12 when x = 22

Graph the equation.

The graph of passes through the origin with a slope of 60.

Answer: