5.5 Direct Variation Pg. 326. Math Pacing Slope Review.

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Presentation transcript:

5.5 Direct Variation Pg. 326

Math Pacing Slope Review

Definition: Direct Variation A Direct Variation is a function in the form … where k does not equal 0.

Definition: Constant of Variation In the equation (function) The constant of variation is k, the coefficient of x.

An equation is a Direct Variation if:  its graph is a line that passes through zero, or  the equation can be written in the form y = kx.

Graphing a Slope with a y-intercept at zero Remember the formula…

Graphing a Slope with a y-intercept at zero Remember the formula…

Example 2-1a 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: k = 2 and m = 2. Slope and Constant of Variation Notice that the slope of the graph of y = kx is k. For a direct variation, the slope and constant of variation are identical. (m = k)

Example 2-1b 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. Slope and Constant of Variation The ordered pair (0, 0) is a solution of y = kx. Therefore, the graph of y = kx passes through the origin. You can use this information to graph direct variation equations. Answer: k = – 4 and m = – 4.

Example 2-1c Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. Answer:constant of variation: 4 ; slope: 4 Slope and Constant of Variation The ordered pair (0, 0) is a solution of y = kx. Therefore, the graph of y = kx passes through the origin. You can use this information to graph direct variation equations.

Example 2-2a Step 1Write the slope as a ratio. Step 2Graph (0, 0). Step 3From the point (0, 0), move up 1 unit and right 1 unit. Draw a dot. Step 4Draw a line containing the points. Direct Variation with k > 0

Example 2-2b Direct Variation with k > 0

Example 2-3a Step 1Write the slope as a ratio. Step 2Graph (0, 0). Step 3From the point (0, 0), move down 3 units and right 2 units. Draw a dot. Step 4Draw a line containing the points. Direct Variation with k < 0

Example 2-3b Direct Variation with k < 0

Example 2-4a Suppose y varies directly as x, andwhen Write a direct variation equation that relates x and y. Find the value of k. Direct variation formula Replace y with 9 and x with –3. Divide each side by –3. Simplify. Answer:Therefore, Write and Solve a Direct Variation Equation

Example 2-4c Use the direct variation equation to find x when Direct variation equation Answer:Therefore, when Replace y with 15. Divide each side by –3. Simplify. Write and Solve a Direct Variation Equation

Example 2-4d Suppose y varies directly as x, andwhen a.Write a direct variation equation that relates x and y. b.Use the direct variation equation to find x when Answer: x = –15 Answer: Write and Solve a Direct Variation Equation

Is an Equation a Direct Variation? If it is, find the constant of variation. 5x + 2y = 0Solve for y. Yes, it’s a direct variation. Constant of variable, k, is

Is an Equation a Direct Variation? If it is, find the constant of variation. 5x + 2y = 9Solve for y. No, it’s not a direct variation. It’s not in the form y = kx.

Is the table a Direct Variation? If it is, find the constant of variation.

Homework Pg. 329, 2 – 34 even