A) \[-\frac{4}{5}\]
B) \[\frac{5}{4}\]
C) \[\frac{4}{5}\]
D) \[-\frac{5}{4}\]
Correct Answer: B
Solution :
Equation of the given line is, \[4x+5y=14.\] Solving the above equation for y, \[y=-\frac{4}{5}x+\frac{14}{5}\] Equate this equation with the point slope formula, \[y=mx+c\] we get \[m=-\frac{4}{5}\] So, slope of the given line is \[m=-\frac{4}{5}\] Now, slope of a line perpendicular to the given line is given as negative reciprocal of the slope of a given line. \[\therefore \] Slope of line perpendicular to the line \[4x+5y=14\] is \[\left( \frac{1}{-4/5} \right)\]
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