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The table represents some points on the graph of a linear function.





x

y


-20
-268


-14
-196


-8
-124


-1
-40




Which equation represents the same relationship?
F 
y+268=(1)/(12)(x+20)
G 
y+20=(1)/(12)(x+268)
H 
y+268=12(x+20)

The table represents some points on the graph of a linear function.\newline\begin{tabular}{|r|c|}\newline\hlinex x & y y \\\newline\hline20-20 & 268-268 \\\newline\hline14-14 & 196-196 \\\newline\hline8-8 & 124-124 \\\newline\hline1-1 & 40-40 \\\newline\hline\newline\end{tabular}\newlineWhich equation represents the same relationship?\newlineF y+268=112(x+20) y+268=\frac{1}{12}(x+20) \newlineG y+20=112(x+268) y+20=\frac{1}{12}(x+268) \newlineH y+268=12(x+20) y+268=12(x+20)

Full solution

Q. The table represents some points on the graph of a linear function.\newline\begin{tabular}{|r|c|}\newline\hlinex x & y y \\\newline\hline20-20 & 268-268 \\\newline\hline14-14 & 196-196 \\\newline\hline8-8 & 124-124 \\\newline\hline1-1 & 40-40 \\\newline\hline\newline\end{tabular}\newlineWhich equation represents the same relationship?\newlineF y+268=112(x+20) y+268=\frac{1}{12}(x+20) \newlineG y+20=112(x+268) y+20=\frac{1}{12}(x+268) \newlineH y+268=12(x+20) y+268=12(x+20)
  1. Calculate slope: Calculate the slope mm using two points from the table. Let's use (20,268)(-20, -268) and (14,196)(-14, -196).m=y2y1x2x1=196(268)14(20)=726=12.m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-196 - (-268)}{-14 - (-20)} = \frac{72}{6} = 12.
  2. Use point-slope form: Use point-slope form to write the equation: yy1=m(xx1)y - y_1 = m(x - x_1). Choose point (20,268)(-20, -268) and slope 1212. \newliney(268)=12(x(20))y - (-268) = 12(x - (-20)).
  3. Simplify equation: Simplify the equation: y+268=12(x+20)y + 268 = 12(x + 20).
  4. Compare with options: Compare the simplified equation with the options given.\newlineThe correct equation is H: y+268=12(x+20)y + 268 = 12(x + 20).

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