4.6 Model Direct Variation
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1 4.6 Model Direct Variation Goal p Write and graph direct variation equations. Your Notes VOCABULARY Direct variation Constant of variation Eample Identif direct variation equations Tell whether the equation represents direct variation. If so, identif the constant of variation. a b. 22 To tell whether an equation represents direct variation, tr to rewrite the equation in the form a. a Write original equation. 2 Subtract from each side. Simplif. Because the equation be rewritten in the form a, it direct variation. The constant of variation is. b. 22 Write original equation. Add to each side. Because the equation 22 be rewritten in the form a, it direct variation. Copright Holt McDougal. All rights reserved. Lesson 4.6 Algebra Notetaking Guide 09
2 4.6 Model Direct Variation Goal p Write and graph direct variation equations. Your Notes VOCABULARY Direct variation The relationship of two variables, and, provided a and a Þ 0 Constant of variation In a, a is called the constant of variation. Eample Identif direct variation equations Tell whether the equation represents direct variation. If so, identif the constant of variation. a b. 22 To tell whether an equation represents direct variation, tr to rewrite the equation in the form a. a Write original equation Subtract 4 from each side. 22 Simplif. Because the equation can be rewritten in the form a, it represents direct variation. The constant of variation is 22. b. 22 Write original equation. 2 Add 2 to each side. Because the equation 22 cannot be rewritten in the form a, it does not represent direct variation. Copright Holt McDougal. All rights reserved. Lesson 4.6 Algebra Notetaking Guide 09
3 Checkpoint Tell whether the equation represents direct variation. If so, identif the constant of variation The graph of a direct variation equation is a line with a slope of a and a -intercept of 0. This line passes through the origin. Eample 2 Graph the direct variation equation. a. b. } a. Plot a point at the origin. The slope is equal to the constant of variation, or. Find and plot a second 2 Graph direct variation equations 2 b. Plot a point at the origin. The slope is equal to the constant of variation, or. Find and plot a second 2 0 Lesson 4.6 Algebra Notetaking Guide Copright Holt McDougal. All rights reserved.
4 Checkpoint Tell whether the equation represents direct variation. If so, identif the constant of variation es; 2 } 4 no The graph of a direct variation equation is a line with a slope of a and a -intercept of 0. This line passes through the origin. Eample 2 Graph the direct variation equation. a. b. } a. Plot a point at the origin. The slope is equal to the constant of variation, or. Find and plot a second 2 Graph direct variation equations 2 (, ) b. Plot a point at the origin. The slope is equal to the constant of variation, or }. Find and plot a second (, ) 2 0 Lesson 4.6 Algebra Notetaking Guide Copright Holt McDougal. All rights reserved.
5 Eample The graph of a direct variation equation is shown. a. Write the direct variation equation. b. Find the value of when (24, 2) a. Because varies directl with, the equation has the form a. Use the fact that 2 when 24 to find a. a Write and use a direct variation equation a( ) Substitute. Write direct variation equation. a Solve for a. A direct variation equation that relates and is. b. When 80,. Checkpoint Complete the following eercises.. Graph the direct variation equation } 2. 2 Homework 4. The graph of a direct variation equation passes through the point (, 24). Write the direct variation equation and find the value of when. Copright Holt McDougal. All rights reserved. Lesson 4.6 Algebra Notetaking Guide
6 Eample The graph of a direct variation equation is shown. a. Write the direct variation equation. b. Find the value of when (24, 2) a. Because varies directl with, the equation has the form a. Use the fact that 2 when 24 to find a. a 2 a( 24 ) Substitute. } 4 Write and use a direct variation equation a Solve for a. Write direct variation equation. A direct variation equation that relates and is } 4. b. When 80, } (80) Checkpoint Complete the following eercises.. Graph the direct variation equation } 2. 2 (2, ) 2 Homework 4. The graph of a direct variation equation passes through the point (, 24). Write the direct variation equation and find the value of when. 2 } 4 ; 220 Copright Holt McDougal. All rights reserved. Lesson 4.6 Algebra Notetaking Guide
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