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Question 70050: Write the equation of the line which has y-intercept (0, 5) and is perpendicular to the line with equation y = –3x + 1.
A) y = 3x + 5 B) y = – x + 5 C) y = x + 5 D) y = –3x + 5
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 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 
.
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:
.
.
.
Therefore, the line perpendicular to the graph of y = -3x + 1 has the slope 
.
In slope intercept form you can begin to write the equation of this perpendicular:
.
.
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:
.
.
This reduces to 
Substitute 5 for b in the equation for the perpendicular line. With this substitution
the equation becomes:
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).
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