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07 Jul 2019, 23:12
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Difficulty:
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Question Stats:
71% (01:39) correct
29%
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based on 120
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If a line L has slope 2 and has y-intercept 5, then what is the equation of line perpendicular to line L and passing through point (1,7)?
A. 2y+x =15
B. 2y+x = 10
C. y=2x+5
D. y=2x-13
E. y+2x=9
A. 2y+x =15
B. 2y+x = 10
C. y=2x+5
D. y=2x-13
E. y+2x=9
09 Jul 2019, 00:41
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A line perpendicular to a line
y = mx + b will have a slope of
y = -(1/m)x + b
Therefore, the slope of a perpendicular line to a line with a slope of 2 will be
-1/2
As we are given that the line will pass through the point (1,7), we can set up the equation of our line as follows
y = -1/2x + b, where y = 7 and x = 1
(7) = -1/2(1) + b
-14 = 1 + 2b
-15 = 2b
-7.5 = b, so
y = -1/2x - 7.5
Looking through the answer choices and changing them to the slope intercept form y = mx + b, answer choice A matches the equation of our new line.
Therefore, A should be the correct choice.
Posted from my mobile device
y = mx + b will have a slope of
y = -(1/m)x + b
Therefore, the slope of a perpendicular line to a line with a slope of 2 will be
-1/2
As we are given that the line will pass through the point (1,7), we can set up the equation of our line as follows
y = -1/2x + b, where y = 7 and x = 1
(7) = -1/2(1) + b
-14 = 1 + 2b
-15 = 2b
-7.5 = b, so
y = -1/2x - 7.5
Looking through the answer choices and changing them to the slope intercept form y = mx + b, answer choice A matches the equation of our new line.
Therefore, A should be the correct choice.
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09 Jul 2019, 01:54
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The line equation is: y = m*x + b
As per the question:
y = 2x +5
Now if a line is a perpendicular then the slope is:
2 * m2 = -1
m2 = -(\(\frac{1}{2}\))
Thus, the line passing through (1,7) and has a slope -1/2 is:
(y-7) = -\(\frac{1}{2}\) * (x - 1)
2 * (y-7) = -x + 1
2y -14 = -x +1
x + 2y = 15
Thus the answer is A.
Please hit kudos if you like the solution.
As per the question:
y = 2x +5
Now if a line is a perpendicular then the slope is:
2 * m2 = -1
m2 = -(\(\frac{1}{2}\))
Thus, the line passing through (1,7) and has a slope -1/2 is:
(y-7) = -\(\frac{1}{2}\) * (x - 1)
2 * (y-7) = -x + 1
2y -14 = -x +1
x + 2y = 15
Thus the answer is A.
Please hit kudos if you like the solution.
