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15 Jun 2022, 09:15
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E
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Difficulty:
15%
(low)
Question Stats:
85% (01:06) correct
15%
(01:10)
wrong
based on 96
sessions
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Referring to the xy-plane above, if the scales on both axes are the same, which of the following could be the equation of line P ?
A. y = 2x/5 - 5/2
B. y = -5x/2 + 5/2
C. y = 5x/2 - 5/2
D. y = 2x/5 + 2/5
E. y = -5x/2 - 5/2
Attachment:
2020-12-14_18-43-29.png [ 9.15 KiB | Viewed 2471 times ]
16 Jun 2022, 01:54
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Referring to the xy-plane above, if the scales on both axes are the same, which of the following could be the equation of line P ?
General equation of a straight line in xy plane is y=mx + c
where m=slope of line and c=intercept of line
Since no co-ordinate of line P is given in question so our aim is to get a general equation of
line P and match it with given options.
Now, c=intercept of line
Intercept is when x=0 what is value of y.
from the diagram we can see that x=0 at y-axis and it is negative
so intercept (c) is negative.
Also, m=slope of line
slope of line is positive when ---> x increases, then y also increases and vice versa
slope of line is negative when ---> x increases, then y decreases.
From diagram, we can see that line P is intersecting at x-axis and y-axis
we can assume point on x-axis as P1(-x,0) and at y-axis as P2(0,-y)
Now when line P goes from P1 to P2 i.e x co-ordinate is changing from -x to 0 so x co-ordinate is increasing.
And when line P goes from P1 to P2 i.e y co-ordinate is changing from 0 to -y so y co-ordinate is decreasing.
From this we can say that slope of line(m) is negative.
From this, we can conclude that general equation of line P can be
y=\(-mx - c\)
Among the options, only E matches the general equation of line P
Hence, E
General equation of a straight line in xy plane is y=mx + c
where m=slope of line and c=intercept of line
Since no co-ordinate of line P is given in question so our aim is to get a general equation of
line P and match it with given options.
Now, c=intercept of line
Intercept is when x=0 what is value of y.
from the diagram we can see that x=0 at y-axis and it is negative
so intercept (c) is negative.
Also, m=slope of line
slope of line is positive when ---> x increases, then y also increases and vice versa
slope of line is negative when ---> x increases, then y decreases.
From diagram, we can see that line P is intersecting at x-axis and y-axis
we can assume point on x-axis as P1(-x,0) and at y-axis as P2(0,-y)
Now when line P goes from P1 to P2 i.e x co-ordinate is changing from -x to 0 so x co-ordinate is increasing.
And when line P goes from P1 to P2 i.e y co-ordinate is changing from 0 to -y so y co-ordinate is decreasing.
From this we can say that slope of line(m) is negative.
From this, we can conclude that general equation of line P can be
y=\(-mx - c\)
Among the options, only E matches the general equation of line P
Hence, E
16 Jun 2022, 09:30
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Bunuel
When we scan the answer choices, we see that all of them are written in slope y-intercept form y = mx + b, where m represents the slope of the line, and b represents the y intercept.
Note: I have rewritten each equation in the precise form y = mx + b
The slope of the line is clearly negative, which means value of m (the slope) must be negative.
This means we can eliminate answer choices A, C and D since they all have positive values of m.
Next, we can see that the y-intercept of the line is negative, which means the value of b (the y-intercept) must be negative.
This means we can eliminate answer choice B, since it has a positive value of b.
By the process of elimination, the answer is E
