So, the line we need to determine is #"perpendicular"# to the given line. Thus, the slope is the #"negative reciprocal"# of the slope of the line given.

Since the line given is in #"slope-intercept form"#, we can easily find the slope as it will be the constant being multiplied to the #x# term. In this line, it will be #-3/7#.

Then, we calculate the #"negative reciprocal"# of it. First negating it, we get #3/7#. Then, taking the reciprocal, it will be #7/3#.

Now, we have our slope of our new line. We are also given a point, so we can use #"point-slope formula"# to determine our new line.

Doing so yields:

#(y-7)=3/7(x-5)#

Now, this is an acceptable form of a line. But since the question gives you a line in #"slope-intercept"# form, you should give your answer in that form as well.

Converting this line to slope intercept, we get:

#y-7=3/7x-15/7#

#y=3/7x-15/7+49/7#

#y=3/7x+34/7#