5.5 Direct Variation Pg. 326.

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Presentation transcript:

5.5 Direct Variation Pg. 326

Algebra 5-2 Slope and Direct Variation Slope Review Math Pacing Harbour

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…

Slope and Constant of Variation 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. 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 2-1a

Slope and Constant of Variation 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 = – 4 and m = – 4. 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 2-1b

Slope and Constant of Variation 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 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 2-1c

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

Direct Variation with k > 0 Example 2-2b

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

Direct Variation with k < 0 Example 2-3b

Write and Solve a Direct Variation Equation Suppose y varies directly as x, and when 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, Example 2-4a

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

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

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

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

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

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

Homework Pg. 329, 2 – 34 even