8th Grade Using Linear Models to Predict Test with Point Values (PDF)

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

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

This 20-point test checks linear models for data, interpreting slope and intercept, and making predictions (Common Core 8.SP.A.3). Work alone, show every step, and write each final answer clearly. You have 45 minutes. Calculators are not needed unless a question says so.

Time and points

About this test

Grade: Grade 8
Chapter: Using Linear Models to Predict
Standards: 8.SP.A.3
Time: 45 minutes
Total: 20 points

Linear model data test: questions

Question 1 – Interpret [3 pts]

A model for the cost $y$ (dollars) of renting a kayak for $x$ hours is $y = 7x + 5$. Interpret the slope and the intercept, and find the cost of 4 hours.

Question 2 – Equation from a graph [3 pts]

Trend line.

A trend line passes through $(0, 10)$ and $(5, 25)$. Write its equation.

Question 3 – Predict [2 pts]

Use $y = 3x + 10$ to predict $y$ when $x = 8$. Is this interpolation or extrapolation if the data have $x$ from 1 to 5?

Question 4 – Find x [3 pts]

Battery model.

Use $y = -12.3x + 100$ to find after how many hours the battery reaches 50 percent. Round to the nearest tenth.

Question 5 – Two points [3 pts]

Two prices.

A scooter rental costs \$11 for 2 hours and \$23 for 5 hours. Assume a linear model. Write the equation and find the cost of 8 hours.

Question 6 – Meaning [2 pts]

A trend line for a hiker’s distance from camp is $y = -2.5x + 10$ (miles after $x$ hours). What does the $x$-value where $y = 0$ tell you? Find it.

Question 7 – Reasonable? [2 pts]

A model predicts that a 4-year-old tree will be 150 feet tall. Explain why you should be careful with this prediction.

Question 8 – Compare [2 pts]

Two models predict the cost of printing $x$ posters: $y = 2x + 10$ and $y = 3x + 4$. For which $x$ do both models give the same cost?

Key facts behind this linear model data test

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

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 8 chapters: Grade 8 math.

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