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In the xy-plane, what is the y-intercept of the line that pa
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11 Feb 2020, 00:53
11 Feb 2020, 00:53
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In the xy-plane, what is the y-intercept of the line that passes through the point (1, −2) and has an x-intercept of 3?
A. 1
B. 0
C. −1
D. −2
E. −3
A. 1
B. 0
C. −1
D. −2
E. −3
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the xy-plane, what is the y-intercept of the line that pa
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12 Feb 2020, 08:23
12 Feb 2020, 08:23
4
huda wrote:
In the xy-plane, what is the y-intercept of the line that passes through the point (1, −2) and has an x-intercept of 3?
A. 1
B. 0
C. −1
D. −2
E. −3
A. 1
B. 0
C. −1
D. −2
E. −3
Show: ::
E
Key concept: If the line has x-intercept 3, then the line crosses the x-axis at the point (3, 0)
So we now know that two points on the line are (1, -2) and (3, 0)
Our goal will be to find the equation of the line in slope y-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept
The slope between the two points = m = rise/run = (0 - -2)/(3 - 1) = 2/2 = 1
Now that we know the slope = 1, we know that the equation of the line is y = 1x + b
At this point we can find the value of b by plugging in the coordinates of one point on the line.
Since (3, 0) is on the line, we can plug x = 3 and y = 0 into the equation to get 0 = 1(3) + b
When we solve this equation for b, we get: b = -3
So the equation of the line is y = x - 3, which means the y intercept (aka b) is -3
Answer: E
Cheers,
Brent
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Status:Founder & Quant Trainer
Affiliations: Prepster Education
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Location: India
WE:Education (Education)
Re: In the xy-plane, what is the y-intercept of the line that pa
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13 Mar 2021, 01:54
13 Mar 2021, 01:54
1
huda wrote:
In the xy-plane, what is the y-intercept of the line that passes through the point (1, −2) and has an x-intercept of 3?
A. 1
B. 0
C. −1
D. −2
E. −3
A. 1
B. 0
C. −1
D. −2
E. −3
Let the equation of line be \(y = mx + c\)
The line passes through (3, 0) and (1, -2)
So, Slope (m) = \(\frac{(-2 - 0)}{(1 - 3)} = 1\)
So, equation of line is \(y = x + c\)
Now, plug \(x =3\) and \(y = 0\)
\(c = -3\)
Hence, option E
