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The equation of a straight line containing the points (10,100) and (15
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31 Oct 2017, 08:21
A wins.
Eq. is y = mx + b
m = (y2- y1)/(x2-x1) = (60-100)/(15-10) = -8
b is value of y when x = 0. Here, x reduces from 15 to 10 when y increases from 60 to 100. So, x will become 0 when y increases by 80. New y = 100 + 80 = 180
2. Now find \(b.\) Use the (x,y) coordinates from one of the two given points. Substitute them into what we have so far: \(y = -8x + b\)
We can substitute because every point on a line (i.e., its coordinates) will satisfy the equation for the line.
I will use (x,y) = (10,100) to find b, the y-intercept:
\(100 = -8(10) + b\) \(100 + 80=b\) \(b = 180\)
\(b\) is positive, so in the original equation, the + sign on the RHS stays the same
We found \(m\) and \(b\). For this question, all we have to do now is put those two values back into the slope-intercept equation, the one we started with.
3) Final: \(y = -8x + 180\)
Answer A
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The equation of a straight line containing the points (10,100) and (15
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31 Oct 2017, 10:00
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Bunuel wrote:
The equation of a straight line containing the points (10,100) and (15, 60) is
(A) y = –8x + 180 (B) y = 8x – 180 (C) y = x/8 + 7.5 (D) y = –8x – 180 (E) y = –x/8 + 22.5
Notice that all of the answers are expressed in slope y-intercept form (y = mx + b, where m represents the line's slope and b represents the line's y-intercept) We can use this to our advantage.
First let's sketch the two points and connect them with a line...
First notice that the slope of the line is NEGATIVE So, we can ELIMINATE answer choices B and C, since those equations represent lines with POSITIVE slopes
Next notice that the y-intercept will be POSITIVE So, we can ELIMINATE answer choice D, since that equation represents a line with a NEGATIVE y-intercept
We're left with answer choices A and E The slope of answer choice A (y = –8x + 180) is -8, and the slope of answer choice E (y = –x/8 + 22.5) is -1/8
From our sketch, we can see that the line is quite steep, so we can ELIMINATE answer choice E, since a slope of -1/8 is not very steep.
Re: The equation of a straight line containing the points (10,100) and (15
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07 May 2019, 18:41
Bunuel wrote:
The equation of a straight line containing the points (10,100) and (15, 60) is
(A) y = –8x + 180 (B) y = 8x – 180 (C) y = x/8 + 7.5 (D) y = –8x – 180 (E) y = –x/8 + 22.5
We know the equation has to be of the form y = mx + b where m and b are constants.
If we let y = 100 and x = 10, we get 10m + b = 100.
If we let y = 60 and x = 15, we get 15m + b = 60.
Subtracting the second equation from the first, we get -5m = 40 and thus m = -8. If we substitute either of the solutions to y = -8x + b, for instance, if we let x = 10 and y = 100, we get b = 180. Thus, the equation of the line is y = -8x + 180.