Direct Variation Equations Review What is the slope

1. What was the greatest speed that Michael traveled? 65 mph

2. What does the horizontal segment of the graph represent? How long does Michael

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

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,

Name the constant of variation for the equation. Then find the slope of the

• The constant of variation is the slope

Y varies directly as x. Find the constant of variation and write an equation

Graph the equation. The graph of slope of 60. Answer: passes through the origin

Slides: 25

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Direct Variation Equations

Review What is the slope?

Slope = 1/2

Slope = -1

Slope = 5

Slope = Undefined

1. What was the greatest speed that Michael traveled? 65 mph

2. What does the horizontal segment of the graph represent? How long does Michael stay at this speed? Constant Speed 70 mins - 20 mins = 50 mins

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

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

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 of variation for the equation. Then find the slope of the line that passes through the pair of points. Slope formula Simplify. Answer: The constant of variation is 2. The slope is 2.

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 of variation: 4; slope: 4

Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. b. Answer: constant of variation: – 3; slope: – 3

• The constant of variation is the slope

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 15 = k(5) Replace y with 15 and x with 5. 15 = k(5) 5 5 Divide each side by 5 3=k Equation? y = 3 x Simplify

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 9 = k(3) 9= k(3) 3 3 Replace y with 15 and x with 5. Divide each side by 5 3=k Equation? y = 3 x Simplify

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 18 = k(11) 18= k(11) 11 11 18 = k 11 Equation? y = 18 x 11 Replace y with 15 and x with 5. Divide each side by 5 Simplify

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 42 = k(7) Replace y with 15 and x with 5. 42= k(7) 7 7 6=k Divide each side by 5 Simplify Equation? y = 6 x

Y varies directly as x. Find the constant of variation and write an equation for the direct variation. 13. y = 12 when x = 22 Find the value of k. Direct variation formula 12 = k(22) 12= k(22) 22 22 6=k 11 Equation? y=6 x 11 Replace y with 15 and x with 5. Divide each side by 5 Simplify

Graph the equation. The graph of slope of 60. Answer: passes through the origin with a