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The equation of a straight line containing the points (10,100) and (15

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The equation of a straight line containing the points (10,100) and (15  [#permalink]

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New post 30 Oct 2017, 23:55
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The equation of a straight line containing the points (10,100) and (15  [#permalink]

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New post 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

Hence, y = -8x + 180
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The equation of a straight line containing the points (10,100) and (15  [#permalink]

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New post 31 Oct 2017, 09:17
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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

We can use the slope-intercept form of a line equation:
\(y = mx + b\)
\(m\) = slope
\(b\) = y-intercept

The answers are all in this form.

1) Find the slope of line from coordinates of the two given points:

\(\frac{rise}{run}=\frac{y2-y1}{x2-x1}=\frac{(100-60)}{10-15}=\frac{40}{-5}= -8 =\) slope

Insert the (-8) where \(m\) is in \(y = mx+b\)

\(y = -8x + b\)

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  [#permalink]

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New post 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...
Image

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.

Answer: A

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Re: The equation of a straight line containing the points (10,100) and (15  [#permalink]

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New post 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.

Answer: A
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Re: The equation of a straight line containing the points (10,100) and (15   [#permalink] 07 May 2019, 18:41
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