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The function 
g is defined by 
g(x)=(1)/(m)x+21, where 
m is an integer constant and 
14 <= m <= 17. For the graph of 
y=g(x)-9 in the 
xy-plane, what is the 
x-coordinate of a possible 
x-intercept?

The function g g is defined by g(x)=1mx+21 g(x)=\frac{1}{m} x+21 , where m m is an integer constant and 14m17 14 \leq m \leq 17 . For the graph of y=g(x)9 y=g(x)-9 in the xy x y -plane, what is the x x -coordinate of a possible x x -intercept?\newlineA) 168-168\newlineB) 192-192\newlineC) 204-204\newlineD) 216-216

Full solution

Q. The function g g is defined by g(x)=1mx+21 g(x)=\frac{1}{m} x+21 , where m m is an integer constant and 14m17 14 \leq m \leq 17 . For the graph of y=g(x)9 y=g(x)-9 in the xy x y -plane, what is the x x -coordinate of a possible x x -intercept?\newlineA) 168-168\newlineB) 192-192\newlineC) 204-204\newlineD) 216-216
  1. Write function y=g(x)y = g(x): First, write the function y=g(x)9y = g(x) - 9. g(x)=1mx+21g(x) = \frac{1}{m}x + 21 y=1mx+219y = \frac{1}{m}x + 21 - 9 y=1mx+12y = \frac{1}{m}x + 12
  2. Find x-intercept: Set yy to 00 to find the xx-intercept. 0=1mx+120 = \frac{1}{m}x + 12
  3. Solve for x: Solve for xx. 1mx+12=0\frac{1}{m}x + 12 = 0 1mx=12\frac{1}{m}x = -12 x=12mx = -12m
  4. Check range of mm: Check the range of mm. 14m1714 \leq m \leq 17
  5. Calculate xx for mm: Calculate xx for each value of mm. For m=14m = 14, x=12imes14=168x = -12 imes 14 = -168 For m=15m = 15, x=12imes15=180x = -12 imes 15 = -180 For m=16m = 16, x=12imes16=192x = -12 imes 16 = -192 For mm00, mm11

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