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x 45 49 53 57 y 10 5 0 -5

\begin{tabular}{rrrrr}\newlinex x & 4545 & 4949 & 5353 & 5757 \\\newline\hliney y & 1010 & 55 & 00 & −5-5\newline\end{tabular}

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Full solution

Q. \begin{tabular}{rrrrr}\newlinex x & 4545 & 4949 & 5353 & 5757 \\\newline\hliney y & 1010 & 55 & 00 & −5-5\newline\end{tabular}
  1. Observe Changes: Step 11: Observe the changes in xx and yy values.xx increases by 44 each time (4545 to 4949, 4949 to 5353, 5353 to 5757).yy decreases by yy11 each time (yy22 to yy11, yy11 to yy55, yy55 to yy77).
  2. Calculate Rate of Change: Step 22: Calculate the rate of change for yy with respect to xx.Change in y=−5\text{Change in } y = -5 (from 1010 to 55)Change in x=4\text{Change in } x = 4 (from 4545 to 4949)Rate of change=Change in yChange in x=−54=−1.25\text{Rate of change} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{-5}{4} = -1.25
  3. Formulate Relationship: Step 33: Formulate the relationship using the slope-intercept form y=mx+by = mx + b.\newlineSlope mm = −1.25-1.25 from Step 22.\newlineUse one point to solve for bb, using point (45,10)(45, 10).\newline10=−1.25(45)+b10 = -1.25(45) + b\newline10=−56.25+b10 = -56.25 + b\newlineb=10+56.25=66.25b = 10 + 56.25 = 66.25
  4. Write Final Equation: Step 44: Write the final equation.\newliney=−1.25x+66.25y = -1.25x + 66.25

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