Which equations represent the line that is perpendicular to the line 5 x minus 2 y is equal to negative 6 and passes through the point open paren 5 comma negative 4 close paren ? Choose three correct answers.

Rewrite 5x − 2y = −6 as y = (5/2)x + 3, so the original line has slope 5/2. A perpendicular line has slope −2/5; through (5, −4), its point-slope equation is y + 4 = −(2/5)(x − 5), which is choice B. Simplifying gives y = −(2/5)x − 2 (choice A), or 2x + 5y = −10 (choice C).

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