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In the rectangular coordinate system, a line passes through the points \((0,5)\) and \((7,0).\) Which of the following

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by Vincen » Tue Jun 30, 2020 7:08 am
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In the rectangular coordinate system, a line passes through the points \((0,5)\) and \((7,0).\) Which of the following points must the line also pass through?

A) \((-14, 10)\)

B) \((-7, 5)\)

C) \((12, -4)\)

D) \((14, -5)\)

E) \((21, -9)\)

[spoiler]OA=D[/spoiler]

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Re: In the rectangular coordinate system, a line passes through the points \((0,5)\) and \((7,0).\) Which of the followi

by Scott@TargetTestPrep » Thu Apr 22, 2021 10:33 am
Vincen wrote: ↑
Tue Jun 30, 2020 7:08 am
 In the rectangular coordinate system, a line passes through the points \((0,5)\) and \((7,0).\) Which of the following points must the line also pass through?

A) \((-14, 10)\)

B) \((-7, 5)\)

C) \((12, -4)\)

D) \((14, -5)\)

E) \((21, -9)\)

[spoiler]OA=D[/spoiler]

Solution:

We see that the slope of the line is (0 - 5) / (7 - 0) = -5/7. Now let’s check each given answer choice by determining the slope between that point and (0, 5).

A. (10 - 5) / (-14 - 0) = 5/(-14) = -5/14 → This is not -5/7.

B. (5 - 5) / (-7 - 0) = 0/(-7) = 0 → This is not -5/7.

C. (-4 - 5) / (12 - 0) = -9/12 = -3/4 → This is not -5/7.

D. (-5 - 5) / (14 - 0) = -10/14 = -5/7 → This is -5/7.

Answer: D

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