Proportionality>Using Trend Lines to Approximate Linear Relationships and Make Predictions(TEKS.Math.8.5.D)
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Texas 8th Grade Math › Proportionality>Using Trend Lines to Approximate Linear Relationships and Make Predictions(TEKS.Math.8.5.D)
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1
A teacher compares study hours ($x$) to test scores ($y$). Approximate trendline: $y = 7.8x + 42$ for $2 \le x \le 10$.
Using the trendline, predict the test score when $x=6$, rounded to the nearest whole number.
47
89
90
136
Explanation
Substitute $x=6$ into $y=7.8x+42$: $y=7.8(6)+42=46.8+42=88.8\approx 89$. Slope-only mistake: $7.8\times 6=46.8\approx 47$ (ignores the intercept). Arithmetic slip: 90 (overestimates $7.8\times 6$ before adding 42). Extrapolation trap: 136 comes from $x=12$ (outside $2\le x\le 10$); predictions outside the data range are unreliable.