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In the xycoordinate system, points (2, 9) and (1, 0) lie on line k.
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23 Aug 2018, 04:59
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In the xycoordinate system, points (2, 9) and (1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n? A. 6 B. 7 C. 8 D. 9 E. 10
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Re: In the xycoordinate system, points (2, 9) and (1, 0) lie on line k.
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23 Aug 2018, 05:06
Bunuel wrote: In the xycoordinate system, points (2, 9) and (1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?
A. 6 B. 7 C. 8 D. 9 E. 10 Equation of the line passing through points (2, 9) and (1, 0): \(y9=\frac{09}{12}*(x2)\) Or, y9=3(x2), this is the equation of the line k If the point (n, 21) lies on line k, then this point must satisfy the above equation. So, 219=3n6 or, 3n6=12 or, 3n=18 or, n=6 Ans. (A)
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In the xycoordinate system, points (2, 9) and (1, 0) lie on line k.
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23 Aug 2018, 20:13
Bunuel wrote: In the xycoordinate system, points (2, 9) and (1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?
A. 6 B. 7 C. 8 D. 9 E. 10 Slopeintercept approach: Find the equation of line \(k\) in slopeintercept form \(y=mx+b\) \(m\) = slope \(b\) = yintercept 1) Find slope. Use the coordinates of the two given points, (2,9) and (1,0) Slope: \(\frac{rise}{run}=\frac{y_2y_1}{x_2x_1}=\frac{09}{12}=\frac{9}{3}=3\)Plug slope into equation: \(y=3x+b\) 2) Find \(b\). Plug (x,y) of either given point into equation. Example (1,0): \(y=3x+b\) \(0=3(1)+b\) \(0=3+b\) \(b=3\) Plug value of \(b\) into equation 3) Full equation of line \(k\) is \(y=3x+3\). Every point (x, y) [and (n, 21)] on a line must satisfy the equation of the line. 4) Point (n, 21) lies on line \(k\) \(n =?\) (n = xcoordinate). Plug in (n, 21) \(y=3x+3\) \(21=3n+3\) \(18=3n\) \(n=6\) Answer A
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Re: In the xycoordinate system, points (2, 9) and (1, 0) lie on line k.
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23 Aug 2018, 22:00
Solution Given:• Points (2, 9) and (1, 0) lie on line k To find:• The value of n such that point (n, 21) also lies on line k. Approach and Working: • Points (2, 9) and (1, 0) lie on line k.
o Hence, slope of line k=\(\frac{{90}}{{2 (1)}}\)= \(\frac{9}{3}\)= 3 • Now, if point (n, 21) also lies on line k then the slope of (n, 21) and(1, 0) will also be equal to 3.
o \(\frac{{210}}{{n+1}}\)= 3 o n=6 Hence, the correct answer is option A. Answer: A
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Re: In the xycoordinate system, points (2, 9) and (1, 0) lie on line k.
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23 Aug 2018, 22:06
Bunuel wrote: In the xycoordinate system, points (2, 9) and (1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?
A. 6 B. 7 C. 8 D. 9 E. 10 Simply use the concept of slope (which many of us think of as Rise/Run)  It is the change in y coordinate for a unit change in x coordinate) (2, 9), (1 , 0)  When x coordinate reduces by 3 units, y coordinate reduces by 9 units (3 times). (1, 0), (n, 21)  So when y coordinate increase by 21 units, x coordinate will increase by 7 units (1/3). So n = 6 Answer (A) For more, check: https://www.veritasprep.com/blog/2016/0 ... linegmat/
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Re: In the xycoordinate system, points (2, 9) and (1, 0) lie on line k.
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