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A certain line on the xy plane contains the points (3,2) and (6,0).
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18 Jul 2022, 16:08
18 Jul 2022, 16:08
Expert Reply
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Question Stats:
70% (00:57) correct
30% (03:00) wrong based on 10 sessions
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A certain line on the xy plane contains the points (3,2) and (6,0). Which of the following points may also be found along this line?
A (1,2)
B (0,4)
C (2,3)
D (3,5)
E (5,6)
A (1,2)
B (0,4)
C (2,3)
D (3,5)
E (5,6)
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
Re: A certain line on the xy plane contains the points (3,2) and (6,0).
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21 Jul 2022, 01:11
21 Jul 2022, 01:11
Expert Reply
A certain line on the xy plane contains the points (3,2) and (6,0).
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24 Jul 2022, 16:21
24 Jul 2022, 16:21
Expert Reply
OE
Quote:
Find the equation of the line in the format y = mx + b, where m is the slope and b is the y-intercept. First find m from the two given points, the rise/run or change in y over the change in x:
m=(0-2)/(6-3)=-2/3
Now find b by using one of the points in the formula and the m just found: y = mx + b, or b = y-mx
Using point (3,2):
b=2-(-2/3)3=2-2=4
so the equation of the line is 𝑦 = (−2/3) 𝑥 + 4. Pause to note that since all of the answer choices have 𝑥 ≥ 0, then the point we are looking for will have 𝑦 ≤ 4. This eliminates choices D and E. Choices A and C can be eliminated because their x-coordinates would result in a fractional y, and none of the given y-coordinates are fractions. Only choice B is left; check it if you have time, otherwise select it and move on. (0,4):
4=(-2/3)0+4
m=(0-2)/(6-3)=-2/3
Now find b by using one of the points in the formula and the m just found: y = mx + b, or b = y-mx
Using point (3,2):
b=2-(-2/3)3=2-2=4
so the equation of the line is 𝑦 = (−2/3) 𝑥 + 4. Pause to note that since all of the answer choices have 𝑥 ≥ 0, then the point we are looking for will have 𝑦 ≤ 4. This eliminates choices D and E. Choices A and C can be eliminated because their x-coordinates would result in a fractional y, and none of the given y-coordinates are fractions. Only choice B is left; check it if you have time, otherwise select it and move on. (0,4):
4=(-2/3)0+4
