Entry Task – SHOW WORK   34 -107

Write and interpret direct variation equations Target: I can Write and interpret direct variation equations

Another way of writing this is k = Definition: Y varies directly as x means that y = kx where k is the constant of variation. Another way of writing this is k = In other words: * the constant of variation (k) in a direct variation is the constant (unchanged) ratio of two variable quantities.

When we talk about a direct variation, we are talking about a relationship where as x increases, y increases or decreases at a CONSTANT RATE.

Direct variation uses the following formula:

Direct Variation example: if y varies directly as x and y = 10 as x =2.4, find x when y =15. what x and y go together?

Direct Variation If y varies directly as x and y = 10 find x when y =15. y = 10, x = 2.4 make these y1 and x1 y = 15, and x = ? make these y2 and x2

Direct Variation if y varies directly as x and y = 10 as x = 2.4, find x when y =15

How do we solve this? Cross multiply and set equal. Direct Variation How do we solve this? Cross multiply and set equal.

Direct Variation We get: 10x = 36 Solve for x by diving both sides by 10. We get x = 3.6

Direct Variation Let’s do another. If y varies directly with x and y = 12 when x = 2, find y when x = 8. Set up your equation.

If y varies directly with x and y = 12 when x = 2, find y when x = 8. Direct Variation If y varies directly with x and y = 12 when x = 2, find y when x = 8.

Cross multiply: 96 = 2y Solve for y. 48 = y. Direct Variation Cross multiply: 96 = 2y Solve for y. 48 = y.

Examples of Direct Variation: Note: X decreases, 10, 5, 3 And Y decreases. 30, 15, 9 What is the constant of variation of the table above? Since y = kx we can say Therefore: 30/10=k or k = 3 15/5=k or k = 3 9/3=k or k =3 Note k stays constant. y = 3x is the equation!

Y varies directly as x. Find the constant of variation and write an equation for the direct variation when y = 42 when x = 7 Find the value of k. y=kx Direct variation formula 42 = k(7) Replace y with 15 and x with 5. 42= k(7) 7 7 Divide each side by 5 6 = k Simplify Equation? y = 6x

Tell if the following graph is a Direct Variation or not. Yes No No No

Tell if the following graph is a Direct Variation or not. 1. 2. Yes No 3. 4. No Yes

Using Direct Variation to find unknowns (y = kx) Given that y varies directly with x, and y = 6 when x=-5, Find y when x = -8. HOW??? 2 step process 1. Find the constant variation. k = y/x or k = 6/-5 = -1.2 k = -1.2 2. Use y = kx. Find the unknown (x). y= -1.2(-8) x= 9.6 Therefore: X =-8 when Y=9.6

Using Direct Variation to solve word problems A car uses 8 gallons of gasoline to travel 290 miles. How much gasoline will the car use to travel 400 miles? Step One: Find points in table Step Three: Use the equation to find the unknown. 400 =36.25x 36.25 36.25 or x = 11.03 Step Two: Find the constant variation and equation: k = y/x or k = 290/8 or 36.25 y = 36.25 x

Homework P. 71 # 7-47 odds Challenge - # 54