8th Grade Linear Functions as Models Worksheet (PDF)

8th Grade math worksheet: Linear Functions as Models – Maths PDF

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This linear function models worksheet for 8th Grade covers linear functions as models (Common Core 8.F.B.4, 8.F.B.5), with a free PDF to print.

These 20 problems practice linear functions as models, rate of change, initial value and graph descriptions (Common Core 8.F.B.4 and 8.F.B.5). Each problem has its own space for work, so print the page and write directly on it.

The problems start with direct skill checks and grow harder as you go. Later items build and interpret models and describe graphs of real situations. Use the answer key afterwards to check every step.

Grade 8 · Common Core State Standards: 8.F.B.4, 8.F.B.5

Linear function models worksheet: exercises 1 to 10

Exercise 1 – Rate from a table

Find the rate of change from the table.

Exercise 2 – Initial value

Find the rate of change and initial value, then write the equation.

Exercise 3 – Interpret an equation

A gym membership costs $y = 4x + 12$ dollars for $x$ visits. Explain what 4 and 12 mean.

Exercise 4 – Two points

A line passes through $(2, 11)$ and $(5, 20)$. Write its equation.

Exercise 5 – Equation from a graph

A line.

Write the equation of the line.

Exercise 6 – Savings model

Jamal has \$50 and adds \$12 each week. Write a function for his savings $S$ after $w$ weeks and find $S$ when $w = 10$.

Exercise 7 – Draining tank

Gallons in a tank over time.

A tank holds 80 gallons and drains 5 gallons each minute. Write the function and find when it is empty.

Exercise 8 – Describe the graph

Graph of a bike ride.

Describe the graph in words, saying where it is increasing, constant and decreasing.

Exercise 9 – Table to equation

A table has the points $(0, 15)$, $(2, 25)$ and $(4, 35)$. Write the linear function.

Exercise 10 – Plant height

The table shows the height of a bean plant in inches. Find the rate of change and the height at week 0.

Exercises 11 and up

Exercise 11 – Bike rental

A bike shop charges \$6 plus \$4 per hour. Write the cost function and find how many hours you can rent for \$30.

Exercise 12 – Constant rate in a table

Find the rate of change from the table: $x = 1, 4, 7$ and $y = 10, 22, 34$.

Exercise 13 – Temperature conversion

The function $F = 1.8C + 32$ converts $^{\circ}\text{C}$ to $^{\circ}\text{F}$. Find $F$ when $C = 20$ and explain what 1.8 means.

Exercise 14 – Gas tank

Gallons left after m miles.

A car’s tank has 14 gallons and uses 0.04 gallon per mile. Write the function, find the gallons left after 250 miles, and find the miles until it is empty.

Exercise 15 – Qualitative curve

Height of a ball over time.

A ball is thrown upward. Is the graph of its height linear or nonlinear? Describe how the height changes.

Exercise 16 – Compare two plans

Plan A cost.

Plan A is shown. Plan B charges \$10 to start and \$18 per month. Which plan has the greater rate? Which costs less after 6 months?

Exercise 17 – Proportional special case

A model has initial value 0. What does that tell you about the relationship?

Exercise 18 – Streaming

A streaming service charged Mei \$27 after 3 months and \$45 after 5 months. Assume a linear model. Find the monthly rate and the sign-up fee.

Exercise 19 – Meaning of an intercept

A line models the water level in a pond: $L = 30 – 2d$ inches after $d$ days. Find the $d$-intercept and explain its meaning.

Exercise 20 – Piecewise story

Maya’s walk to the store.

The graph shows Maya’s distance from home. Describe what she did in each part of the trip.

Key facts behind this linear function models worksheet

Key facts

Rate of change $m = \frac{\text{change in } y}{\text{change in } x}$; initial value $b$ is $y$ when $x = 0$.
Build a model: find $m$, solve for $b$ with one point, write $y = mx + b$.
A negative rate means the quantity decreases.
A flat segment has rate 0; a curve means the rate is not constant.
Always say what $m$ and $b$ mean in the situation, with units.

How to use this linear function models worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the linear function models worksheet as a PDF with the button below and keep it with your notes.

All Grade 8 chapters: Grade 8 math.

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