SOLUTION: write the equation of the lne which has y-intercept (0,5) and is perpendicular to line with equation Y=-3x+1

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Question 110284: write the equation of the lne which has y-intercept (0,5) and is perpendicular to line with equation Y=-3x+1
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
In this problem use the slope-intercept form of an equation. The slope-intercept form is:
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y = mx + b
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where m is the slope of the line and b is the value of y where the line intercepts the y-axis.
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You are given the equation:
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y = -3x + 1
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By comparing this equation to the slope-intercept form, you can see that the multiplier of
the x term is -3 and therefore is equal to m, the slope of the line.
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Next you need to know that any line perpendicular to this line will have a slope that is the
negative reciprocal of the slope. Since the slope of the given line is -3, the slope of
the perpendicular line will be ... the negative reciprocal of -3. This
slope of the perpendicular line simplifies to when the two negative signs are
taken into account.
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Therefore, we can write that the line perpendicular to the given line has an equation of:
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where b is the value of y where the line intercepts the y-axis. The problem tells you
that the y-intercept is at the point (0, 5) so the value of y at this point is +5 and that is
the value of b. Substituting +5 for b results in the equation becoming:
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and this is the equation you were asked to find.
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As added info, let's look at the two graphs. The red graph is the graph of the given equation
and the green graph is the graph of the perpendicular equation we found:
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Hope this helps you to understand the problem. Probably the most important lesson to
learn in this problem is that if two lines are perpendicular, their slopes are negative
inverses of each other. If one slope is , the slope of the perpendicular line is .
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