For this case we have to by definition, if two lines are perpendicular then the product of its slopes is -1.
We have the following line:
[tex]14x-7y = 8[/tex]
Rewriting:
[tex]-7y = 8-14x\\7y = 14x-8\\y = 2x- \frac {8} {7}[/tex]
Thus, the slope is:
[tex]m_ {1} = 2[/tex]
We have to:
[tex]m_ {1} * m_ {2} = - 1[/tex] (Perpendicular condition)
[tex]2 * m_ {2} = - 1[/tex]
[tex]m_ {2} = - \frac {1} {2}[/tex]
Thus, the equation of the line is:
[tex]y = - \frac {1} {2} x + b[/tex]
We find "b" knowing that the line passes through the point (-2,5).
[tex]5 = - \frac {1} {2} (- 2) + b\\5 = 1 + b\\b = 5-1 = 4[/tex]
Finally, the equation is:
[tex]y = - \frac {1} {2} x + 4[/tex]
Answer:
[tex]y = - \frac {1} {2} x + 4[/tex]
