Write an equation for a line that passes through (8,-8) and is perpendicular to 5 x + 8 y = 26 5 x + 8 y = 26 5 x + 8 y = 26 .A) y = − 5 8 x − 56 5 y = - \frac { 5 } { 8 } x - \frac { 56 } { 5 } y = − 8 5 x − 5 56 B) y = − 5 8 x − 104 5 y = - \frac { 5 } { 8 } x - \frac { 104 } { 5 } y = − 8 5 x − 5 104 C) y = − 8 5 x − 104 5 y = - \frac { 8 } { 5 } x - \frac { 104 } { 5 } y = − 5 8 x − 5 104 D) y = 5 8 x + 104 5 y = \frac { 5 } { 8 } x + \frac { 104 } { 5 } y = 8 5 x + 5 104 E) y = 8 5 x − 104 5 y = \frac { 8 } { 5 } x - \frac { 104 } { 5 } y = 5 8 x − 5 104

Question

Write an equation for a line that passes through (8,-8)  and is perpendicular to   5 x + 8 y = 26 5 x + 8 y = 26 5 x + 8 y = 26   .A)    y = − 5 8 x − 56 5 y = - \frac { 5 } { 8 } x - \frac { 56 } { 5 } y = − 8 5 ​ x − 5 56 ​ B)    y = − 5 8 x − 104 5 y = - \frac { 5 } { 8 } x - \frac { 104 } { 5 } y = − 8 5 ​ x − 5 104 ​ C)    y = − 8 5 x − 104 5 y = - \frac { 8 } { 5 } x - \frac { 104 } { 5 } y = − 5 8 ​ x − 5 104 ​ D)    y = 5 8 x + 104 5 y = \frac { 5 } { 8 } x + \frac { 104 } { 5 } y = 8 5 ​ x + 5 104 ​ E)    y = 8 5 x − 104 5 y = \frac { 8 } { 5 } x - \frac { 104 } { 5 } y = 5 8 ​ x − 5 104 ​

Nayan Shrivastava · Accepted Answer

Final Answer : E, Explanation :   The slope of the line   5 x + 8 y = 26 5x + 8y = 26 5 x + 8 y = 26   is   − 5 8 -\frac{5}{8} − 8 5 ​  . A line perpendicular to it will have a slope of   8 5 \frac{8}{5} 5 8 ​  . Using the point-slope form with point (8, -8), the equation is   y + 8 = 8 5 ( x − 8 ) y + 8 = \frac{8}{5}(x - 8) y + 8 = 5 8 ​ ( x − 8 )  , which simplifies to   y = 8 5 x − 104 5 y = \frac{8}{5}x - \frac{104}{5} y = 5 8 ​ x − 5 104 ​  .

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