Perpendicular lines always have slopes that are opposite reciprocals of one another. To find the slope of the equation, we need to find the opposite reciprocal of the slope of #2x-y=7#. To do so, we need to put #2x-y=7# in slope intercept form.
#-y=7-2x rarr# Isolate the y variable
#y=-7+2x rarr# Divide each side by -1
#y=2x-7 rarr# The equation shows that this line's slope is 2 (the slope-intercept form of an equation is written as y=ax+b, where a is the slope and b is the y-intercept).
The opposite reciprocal of 2 is #-1/2# (the opposite of a positive number is negative and vice versa, the reciprocal of a number is its numerator and denominator switched).
We now know that the equation has a slope of #-1/2#, but we do not know its y-intercept. To find the intercept, we can write an equation using the variable b to represent the unknown number.
#5=-1/2*2+b rarr# The line passes through (2, 5), so we can plug those numbers in for x and y.
#5=-1+b rarr# Simplify
#b=6 rarr# Solve for b, the y-intercept.
The equation is #y=-1/2*x+6#
