4.6 model direct variation day 1
- 1. Direct Variation Section 4.6 Page 253
- 2. • When x and y vary directly, there is a nonzero number a such that the following is true: y = ax a is the constant of variation For example: y = 3x or y = -1/4x non-example : y = 4x + 5
- 3. • y = ax shows direct variation between x & y • What else is true about this type of equation? • YES = it goes through the origin!
- 4. EXAMPLE 1 Identify direct variation equations Tell whether the equation represents direct variation. If so, identify the constant of variation. a. 2x – 3y = 0 b. – x + y = 4
- 5. EXAMPLE 1 Identify direct variation equations SOLUTION To tell whether an equation represents direct variation, try to rewrite the equation in the form y = ax. 2x – 3y = 0 Write original equation. – 3y = – 2x Subtract 2x from each side. 2x Simplify. y= 3 ANSWER Because the equation 2x – 3y = 0 can be rewritten in the form y = ax, it represents direct variation. The constant of variation is. 2 3
- 6. EXAMPLE 1 Identify direct variation equations b. –x+y=4 Write original equation. y = x+4 Add x to each side. ANSWER Because the equation – x + y = 4 cannot be rewritten in the form y = ax, it does not represent direct variation.
- 7. EXAMPLE 2 Graph direct variation equations Graph the direct variation equation. 2 a. y = x b. y = – 3x 3 SOLUTION a. Plot a point at the origin. The slope is equal to the constant of variation, or 2 Find and plot a second 3 point, then draw a line through the points.
- 8. EXAMPLE 2 Graph direct variation equations b. Plot a point at the origin. The slope is equal to the constant of variation, or – 3. Find and plot a second point, then draw a line through the points.
- 9. What can you tell about these two lines? Let’s look at the graph Y =3x (red) Y = -2x (blue) What is the slope of each line above?
- 10. Graph these equations Y = - 3x Y = 0.4 x
- 11. EXAMPLE 3 Write and use a direct variation equation The graph of a direct variation equation is shown. a. Write the direct variation equation. b. Find the value of y when x = 30. SOLUTION a. Because y varies directly with x, the equation has the form y = ax. Use the fact that y = 2 when x = – 1 to find a. y = ax Write direct variation equation. 2 = a (– 1) Substitute. –2=a Solve for a.
- 12. • Assignment: • P. 256 (#1-15, 19-20) • You will need graph paper