Write and graph a direct variation equation

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Presentation transcript:

Write and graph a direct variation equation EXAMPLE 1 Write and graph a direct variation equation Write and graph a direct variation equation that has (– 4, 8) as a solution. SOLUTION Use the given values of x and y to find the constant of variation. y = ax Write direct variation equation. 8 = a(– 4) Substitute 8 for y and – 4 for x. –2= a Solve for a.

EXAMPLE 1 Write and graph a direct variation equation ANSWER Substituting – 2 for a in y = ax gives the direct variation equation y = – 2x. Its graph is shown.

Use the given values of x and y to find the constant of variation. GUIDED PRACTICE for Example 1 Write and graph a direct variation equation that has the given ordered pair as a solution. (3, – 9) SOLUTION Use the given values of x and y to find the constant of variation. y = ax Write direct variation equation. –9 = a(3) Substitute – 9 for y and 3 for x. –3= a Solve for a.

GUIDED PRACTICE for Example 1 ANSWER Substituting – 3 for a in y = ax gives the direct variation equation y = – 3x. Its graph is shown.

Use the given values of x and y to find the constant of variation. GUIDED PRACTICE for Example 1 Write and graph a direct variation equation that has the given ordered pair as a solution. (– 7, 4) SOLUTION Use the given values of x and y to find the constant of variation. y = ax Write direct variation equation. 4 = a(– 7) Substitute 4 for y and – 7 for x. – 4 7 = a Solve for a.

GUIDED PRACTICE for Example 1 ANSWER Substituting for a in y = ax gives the direct variation equation y = x. Its graph is shown. 7 – 4

Use the given values of x and y to find the constant of variation. GUIDED PRACTICE for Example 1 Write and graph a direct variation equation that has the given ordered pair as a solution. (5, 3) SOLUTION Use the given values of x and y to find the constant of variation. y = ax Write direct variation equation. 3 = a(5) Substitute 3 for y and 5 for x. = a 5 3 Solve for a.

GUIDED PRACTICE for Example 1 ANSWER Substituting for a in y = ax gives the direct variation equation y = x. Its graph is shown. 5 3

Use the given values of x and y to find the constant of variation. GUIDED PRACTICE for Example 1 Write and graph a direct variation equation that has the given ordered pair as a solution. (6, – 2) SOLUTION Use the given values of x and y to find the constant of variation. y = ax Write direct variation equation. – 2 = a(6) Substitute – 2 for y and 6 for x. = a 3 – 1 Solve for a.

GUIDED PRACTICE for Example 1 ANSWER Substituting for a in y = ax gives the direct variation equation y = x. Its graph is shown. 3 – 1