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Question 91498: A line passing through (-8, 2) and (-1,y) is perpendicular to a line with slope -7/5. Find the value of y.
I worked it out to be y=7.
Is this correct?
Thanks so much!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Your answer is correct!
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Here's a brief description of a way you might have used.
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Given that a line has a slope of -7/5. Its equation could be y = (-7/5)*x.
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A line that is perpendicular to this line would have a slope that is the negative inverse of
-7/5. The negative inverse of this slope is +5/7. Therefore, in slope intercept form the
equation of a line having a slope of +5/7 is:
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y = (+5/7)x + b
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From the problem you know that the point (-8,2) is satisfies this equation. If you substitute
-8 for x and +2 for y, you can solve for b. After the substitutions, the equation becomes:
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2 = (+5/7)*(-8) + b
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Do the multiplication on the right side and you get:
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2 = (-40/7) + b
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Get rid of the -40/7 on the right side by adding + 40/7 to both sides and you get:
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2 + 40/7 = b
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Recognize that 2 is equal to 14/7. Substitute 14/7 for 2 and the equation is then:
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14/7 + 40/7 = 54/7 = b
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Return to our equation for the perpendicular line and substitute 54/7 for b to make the
equation become:
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y = (5/7)*x + 54/7
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Now you can use this point to find the value of y in the point (-1, y). This point will
be on the graph so when x is -1, we need to find the value of y from the equation.
In the equation substitute -1 for x and the equation becomes:
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y = (5/7)*(-1) + 54/7
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Do the multiplication on the right side:
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y = (-5/7) + 54/7
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Add the two terms and you get:
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y = 49/7 = 7
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Your answer of 7 is correct.
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Hope this shows you an understandable method that you might have used in solving your problem.
If you used a different method (and there are other ways you might have used), maybe this
method will help you to understand the problem a little more. Anyhow, good work! You used
a method that worked! Cheers.
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