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# What is the equation of the line that passes through the points (−4, 3

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Math Expert
Joined: 02 Sep 2009
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What is the equation of the line that passes through the points (−4, 3  [#permalink]

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25 Feb 2019, 02:33
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91% (01:15) correct 9% (01:09) wrong based on 46 sessions

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What is the equation of the line that passes through the points (−4, 3) and (6, −2) ?

A. y = −1/2*x + 1
B. y = −1/2*x + 2
C. y = 1/2*x + 5
D. y = 1/2*x + 7
E. y = 1/2*x + 8

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Re: What is the equation of the line that passes through the points (−4, 3  [#permalink]

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25 Feb 2019, 02:47
3 = -4k + n
-2 = 6k + n

You can do the system and have -10k=5, k=-1/2, then calculate n from an equation and get +1. Therefore A

Or you can consider the faster approach.

You draw the line in the coordinate plane just to see how it is going down, and therefore the k must be negative. Eliminate C, D and E as k is positive.

Now plug in the values of given points into option A -> correct, or plug in the values in B -> incorrect -> therefore A is correct.
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Re: What is the equation of the line that passes through the points (−4, 3  [#permalink]

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25 Feb 2019, 04:34
Bunuel wrote:
What is the equation of the line that passes through the points (−4, 3) and (6, −2) ?

A. y = −1/2*x + 1
B. y = −1/2*x + 2
C. y = 1/2*x + 5
D. y = 1/2*x + 7
E. y = 1/2*x + 8

use formula

y-y1/x-x1= y2-y1/x2-x1
solve
we get
y = −1/2*x + 1
IMO A
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Re: What is the equation of the line that passes through the points (−4, 3  [#permalink]

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04 Mar 2019, 08:50
Bunuel wrote:
What is the equation of the line that passes through the points (−4, 3) and (6, −2) ?

A. y = −1/2*x + 1
B. y = −1/2*x + 2
C. y = 1/2*x + 5
D. y = 1/2*x + 7
E. y = 1/2*x + 8

First, let's determine the slope, using the two ordered pairs:

Slope = (y2 - y1)/(x2 - x1) = (-2 - 3)/(6 - (-4)) = -5/10 = -1/2

Next we can determine the y-intercept. We could use either ordered pair to get the x and y values to substitute into the slope-intercept form of the line, but we choose (6, -2).

-2 = (6)(-1/2) + b

-2 = -3 + b

1 = b

Thus, the equation is y = −1/2*x + 1.

Alternate Solution:

Letting the equation of the line be y = mx + n, we note that both of these points must satisfy this equation since they are on this line.

From the first point, substituting x = -4 and y = 3, we obtain the equation 3 = -4m + n.

From the second point, substituting x = 6 and y = -2, we obtain the equation -2 = 6m + n.

Subtracting the second equation from the first, we find that 5 = -10m; therefore m = -1/2.

Multiplying the first equation by 3/2 and adding to the second equation, we find 9/2 - 2 = 3n/2 + n. Simplifying, we get 5/2 = 5n/2; which implies n = 1.

Thus, the equation of the line is y =-1/2*x + 1.

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Re: What is the equation of the line that passes through the points (−4, 3   [#permalink] 04 Mar 2019, 08:50
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