The table represents some points on the graph of a linear function.\begin{tabular}{|r|c|}\hlinex & y \\\hline−20 & −268 \\\hline−14 & −196 \\\hline−8 & −124 \\\hline−1 & −40 \\\hline\end{tabular}Which equation represents the same relationship?F y+268=121(x+20)G y+20=121(x+268)H y+268=12(x+20)
Q. The table represents some points on the graph of a linear function.\begin{tabular}{|r|c|}\hlinex & y \\\hline−20 & −268 \\\hline−14 & −196 \\\hline−8 & −124 \\\hline−1 & −40 \\\hline\end{tabular}Which equation represents the same relationship?F y+268=121(x+20)G y+20=121(x+268)H y+268=12(x+20)
Calculate slope: Calculate the slope m using two points from the table. Let's use (−20,−268) and (−14,−196).m=x2−x1y2−y1=−14−(−20)−196−(−268)=672=12.
Use point-slope form: Use point-slope form to write the equation: y−y1=m(x−x1). Choose point (−20,−268) and slope 12. y−(−268)=12(x−(−20)).
Simplify equation: Simplify the equation: y+268=12(x+20).
Compare with options: Compare the simplified equation with the options given.The correct equation is H: y+268=12(x+20).
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