Lines of Best Fit and Linear Models: Grade 8 Math Test – PDF Download

Question 1: Judge the fit (2 points)

Maya tracks her savings. The graph shows her balance after each week and the line \(y=15x+22\).

1. How many points are above the line, below the line, and on the line? (1 point)
2. Is the line a good fit? Explain. (1 point)

Question 2: Equation of the line (2 points)

The graph shows the cost of a pottery class. The line passes through the two labeled points. Write the equation of the line in the form \(y=mx+b\).

Question 3: Meaning in context (2 points)

The cost \(C\) in dollars of renting a kayak for \(h\) hours is modeled by \(C=12h+8\).

1. Explain what 12 means. (1 point)
2. Explain what 8 means. (1 point)

Question 4: Predict and compare (2 points)

The line \(V=-2x+26\) models the value \(V\) (in thousands of dollars) of a car that is \(x\) years old.

1. Find the predicted value of a 6-year-old car. (1 point)
2. A 6-year-old car actually sold for $15,000. Is that above or below the prediction, and by how much? (1 point)

Question 5: Is a line appropriate? (2 points)

The graph shows speed and braking distance for a car. The straight line passes through the first and last points.

1. Describe how the middle points compare with the line. (1 point)
2. Is a linear model appropriate? Explain. (1 point)

Question 6: Better line (2 points)

A data set has the points \((1,5)\), \((2,9)\), \((3,12)\), \((4,17)\) and \((5,20)\). Jamal proposes \(y=4x+1\). Aisha proposes \(y=5x\). Which line fits better? Justify with the vertical gaps.

Question 7: Candle model (3 points)

The length \(L\) of a candle in inches after burning \(t\) hours is modeled by \(L=-0.8t+12\), based on data from 0 to 10 hours.

1. Explain what the slope and y-intercept mean. (1 point)
2. Predict the length after 7.5 hours. (1 point)
3. After how many hours does the model predict the candle is gone? (1 point)

Question 8: Gaps and outlier (3 points)

Ethan records the hours \(x\) he spends on screens and his score \(y\) on a short quiz: \((1,91)\), \((2,84)\), \((3,80)\), \((4,60)\), \((5,71)\), \((6,64)\). A line of fit is \(y=-5x+95\).

1. Find the predicted score and the gap (actual minus predicted) for each point. (2 points)
2. Identify the outlier. (1 point)

Question 9: Reliable prediction? (2 points)

After 1 to 8 weeks of training, Noah’s 5K time \(T\) in minutes fits the model \(T=-0.5w+30\), where \(w\) is the number of weeks.

1. Predict the time after 70 weeks. (1 point)
2. Explain why this prediction is not reasonable. (1 point)

⬇ Download the Grade 8 Lines of Best Fit and Linear Models test (PDF, 96 KB)

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