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# In a rectangular coordinate system, which of the following

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Re: In a rectangular coordinate system ............ [#permalink]
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pzazz12 wrote:
In a rectangular coordinate system ,which of the following points is intersected by the line connected by the coordinates (5,6) and(21,18)?
A.(9,9)
B.(12,12)
C.(13,13)
D.(12,13)
E.(16,15)

Equation of the line connecting the two points,(5,6) and (21,18);

y-6= {(6-18)/(5-21)}(x-5) or , 4y-3x=9

Only ( 9,9) is satisfying the equation.Hence answer is A.

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In a rectangular coordinate system, which of the following [#permalink]
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I found the equation of the line to be $$y = \frac{3x}{4} + \frac{9}{4}.$$. Then, noticing that 3 of the options had the same value for x and y, I wanted to check at which point on the line the x and y values were equal. So I solved for x:

$$x = \frac{3x}{4} + \frac{9}{4}$$
$$\frac{x}{4} = \frac{9}{4}.$$
$$x = 9.$$

Therefore, (9,9) is a point on the line and our answer is A.

Further: If we would have found some other value (one that wasn't listed on the answer choices) then we at least could have eliminated 3 of the answer choices and then manually checked the other two.
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Re: In a rectangular coordinate system, which of the following [#permalink]
equation of line: y-6 = {(18-6)/(21-5)} (x-5)
rearranging we get 4y-3x = 9. Put the co ordinates, given in the option, in the equation.

we will get (9,9) as answer

Option A
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Re: In a rectangular coordinate system, which of the following [#permalink]
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pzazz12 wrote:
In a rectangular coordinate system, which of the following points is intersected by the line connected by the coordinates (5,6) and (21,18)?

A. (9,9)
B. (12,12)
C. (13,13)
D. (12,13)
E. (16,15)

Let’s first create the equation of a line for coordinates (5,6) and (21,18).

Slope = Δy/Δx = 12/16 = 3/4.

We can substitute in either ordered pair to calculate the y-intercept. Let’s use (5,6):

y = (3/4)x + b

6 = (3/4)(5) + b

6 = 15/4 + b

24/4 = 15/4 + b

9/4 = b

Thus, y = (3/4)x + 9/4

Let’s now substitute each set of coordinates to see which holds true in our equation.

A) (9,9)

9 = (3/4)(9) + 9/4 ?

9 = 27/4 + 9/4 ?

9 = 36/4 ?

9 = 9 ? → Yes!

Answer: A
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Re: In a rectangular coordinate system, which of the following [#permalink]
Can someone solve this using graph?
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Re: In a rectangular coordinate system, which of the following [#permalink]
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Re: In a rectangular coordinate system, which of the following [#permalink]
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