Question 70050
The most important thing to note is that if you are given a line with a slope m, the slope
of a line that is perpendicular to it is {{{-1/m}}}

.
You are given the line y = -3x + 1.  This is in the form of the slope-intercept equation which
is the form y = mx + b.  In this slope-intercept equation m is the slope.  By comparing the given equation to
the slope-intercept form you can see that the slope m in the given equation is -3.  Therefore,
a line perpendicular to the graph of the given equation is the negative inverse of -3.  The 
slope of the perpendicular line, therefore, is:
.

{{{-1/-3 = +1/3}}}
.
.
Therefore, the line perpendicular to the graph of y = -3x + 1 has the slope {{{1/3}}}
.

In slope intercept form you can begin to write the equation of this perpendicular:
.

{{{y = (1/3)x + b}}}
.
 
The one thing we know about this line is that it goes through the point (0,5).  So if you
go to the above, 
beginning of our perpendicular equation and substitute 0 for x and 5 for y the equation becomes:
.
{{{5 = (1/3)*0 + b}}}
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This reduces to {{{5 = b}}}

Substitute 5 for b in the equation for the perpendicular line.  With this substitution
the equation becomes:

{{{y = (1/3)x + 5}}}

Trust me, this is correct.  However, it does not match any of the answers listed.  Somebody
made a mistake.  If you have doubts, graph the given equation and the above equation
for the perpendicular line and you will see they are perpendicular, and the perpendicular
line goes through (0,5).