1. Bellringer Put your name at the top of the paper 1. Is the set {(2,0), (-1, 9), (4,-2), (3,0), (1,9)} a function? 2. Find the slope of the line that passes through the following points, (9,4) and (3,2). 3. Write in standard form an equation of the line with slope -3 through the point (-2,6). 4. Write y = 7x – 2 in standard form. 5. What is the y-intercept of equation y = 2x +6?

2. 2-3 Direct Variation M11.A.2.1.2: Solve problems using direct and inverse proportions M11.D.4.1.1: Match the graph of a given function to its table or equation

3. Objectives Writing and Interpreting a Direct Variation

4. Vocabulary A linear function defined by an equation of the form y = kx, where k ≠ 0, represents direct variation. When x and y are variables, you can write k =, so the ration y : x equals the constant k, the constant of variation.

5. Identifying Direct Variation From a Table For each function, determine whether y varies directly with x. If so, find the constant of variation and write the equation. x–1 2 5 y 3–615 a. Since the three ratios are not all equal, y does not vary directly with x. x 7 9–4 y1418–8 b. The constant of variation is 2. The equation is y = 2x. = and are both equal to –3, but = 3. yxyx 3 –1 –6 2 15 5 = 2, so y does vary directly with x. yxyx 14 7 18 9 –8 –4 ===

6. Identifying Direct Variation From an Equation For each function, tell whether y varies directly with x. If so, find the constant of variation. a.3y = 7x + 7 Since you cannot write the equation in the form y = kx, y does not vary directly with x. b.5x = –2y 5x = –2y is equivalent to y = – x, so y varies directly with x. 5252 The constant of variation is –. 5252

7. The perimeter of a square varies directly as the length of a side of the square. The formula P = 4s relates the perimeter to the length of a side. a.Find the constant of variation. The equation P = 4s has the form of a direct variation equation with k = 4. b.Find how long a side of the square must be for the perimeter to be 64 cm. P = 4sUse the direct variation. 64 = 4sSubstitute 64 for P. 16 = sSolve for s. The sides of the square must have length 16 cm. Real World Example

8. Suppose y varies directly with x, and y = 15 when x = 27. Find y when x = 18. Let (x 1, y 1 ) = (27, 15) and let (x 2, y 2 ) = (18, y). 15(18) = 27(y)Write the cross products. y = 10Simplify. Write a proportion. y1x1y1x1 y2x2y2x2 = Substitute. = 15 27 y 18 y = Solve for y. 15 18 27 Using Proportion

9. Homework Pg 74 & 75 #1,2,9,10,17,18,23,24,25