8th Grade Using Linear Models to Predict Test Solutions and Scoring (PDF)

8th Grade math test solutions: Using Linear Models to Predict – Maths PDF

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This linear model data test answers for 8th Grade covers using linear models to predict (Common Core 8.SP.A.3), with a free PDF to print.

Use this answer key to score the linear models for data test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.SP.A.3

Linear model data test answers: worked solutions

Question 1 – Interpret [3 pts]

Slope: \$7 per hour. Intercept: a \$5 fee. $y = 7 \cdot 4 + 5 = 33$.

Scoring: 1 point for each interpretation. 1 point for \$33.

Question 2 – Equation from a graph [3 pts]

Line y = 3x + 10.

$m = \frac{25 – 10}{5} = 3$, $b = 10$.

$y = 3x + 10$

Scoring: 1 point for the slope, 1 point for the intercept, 1 point for the equation.

Question 3 – Predict [2 pts]

$3 \cdot 8 + 10 = 34$. It is extrapolation, since 8 is outside the data.

Scoring: 1 point for 34. 1 point for extrapolation.

Question 4 – Find x [3 pts]

The line reaches 50 at about 4.1 hours.

$50 = -12.3x + 100$, so $x = \frac{50}{12.3} \approx 4.1$.

Scoring: 1 point for the equation, 1 point for solving, 1 point for 4.1 hours.

Question 5 – Two points [3 pts]

$m = \frac{23 – 11}{5 – 2} = 4$. $11 = 4 \cdot 2 + b$, so $b = 3$. $y = 4x + 3$.

8 hours: $4 \cdot 8 + 3 = 35$.

Scoring: 1 point for the slope, 1 point for the equation, 1 point for \$35.

Question 6 – Meaning [2 pts]

$0 = -2.5x + 10$, so $x = 4$. After 4 hours the hiker is back at camp.

Scoring: 1 point for 4. 1 point for the meaning.

Question 7 – Reasonable? [2 pts]

The model may only fit trees in a smaller range, and extrapolating beyond the data can give unrealistic results.

Scoring: 1 point for extrapolation. 1 point for a clear explanation.

Question 8 – Compare [2 pts]

$2x + 10 = 3x + 4$, so $x = 6$.

Scoring: 1 point for the equation. 1 point for $x = 6$.

Total score

Total

20 points

Key facts behind this linear model data test answers

Key facts

Slope: the predicted change in $y$ per 1-unit increase in $x$, with units.
Intercept: the predicted $y$ when $x = 0$, if that is meaningful.
Find the equation from two points on the trend line.
Predict by substituting $x$; find $x$ from a target $y$ by solving an equation.
Be cautious when predicting far outside the data range.

How to use this linear model data test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 8 chapters: Grade 8 math.

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