8th Grade Linear Functions as Models Worksheet Solutions (PDF)

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

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

This answer key gives a full worked solution for each of the 20 problems on the linear function models worksheet (Common Core 8.F.B.4 and 8.F.B.5). Compare each step with your own work, not only the final answer, and note any step where your method differed.

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

Linear function models answers: exercises 1 to 10

Exercise 1 – Rate from a table

$\frac{11 – 5}{3 – 1} = \frac{6}{2} = 3$.

$3$

Exercise 2 – Initial value

Rate: $\frac{13 – 7}{2 – 0} = 3$. Initial value (at $x = 0$): 7.

$y = 3x + 7$

Exercise 3 – Interpret an equation

4 is the rate: \$4 for each visit. 12 is the initial value: a \$12 fee when there are 0 visits.

\$4 per visit; \$12 starting fee

Exercise 4 – Two points

$m = \frac{20 – 11}{5 – 2} = 3$.

$11 = 3 \cdot 2 + b$, so $b = 5$.

$y = 3x + 5$

Exercise 5 – Equation from a graph

Rise 6, run 3.

$m = \frac{6}{3} = 2$; the y-intercept is 4.

$y = 2x + 4$

Exercise 6 – Savings model

Savings after 10 weeks.

$S = 12w + 50$.

$S = 12 \cdot 10 + 50 = 170$.

\$170

Exercise 7 – Draining tank

$V = 80 – 5t$.

$0 = 80 – 5t$, so $t = 16$.

$V = 80 – 5t$; empty at 16 minutes

Exercise 8 – Describe the graph

From 0 to 2 hours it increases, from 2 to 4 hours it is constant, and from 4 to 6 hours it decreases.

Increasing, then constant, then decreasing

Exercise 9 – Table to equation

Rate: $\frac{25 – 15}{2 – 0} = 5$. Initial value: 15.

$y = 5x + 15$

Exercise 10 – Plant height

Rate: $\frac{18 – 9}{5 – 2} = 3$ inches per week.

$9 = 3 \cdot 2 + b$, so $b = 3$.

3 inches per week; 3 inches at week 0

Exercises 11 and up

Exercise 11 – Bike rental

$C = 4h + 6$.

$30 = 4h + 6$, so $h = 6$.

$C = 4h + 6$; 6 hours

Exercise 12 – Constant rate in a table

$\frac{22 – 10}{4 – 1} = 4$ and $\frac{34 – 22}{7 – 4} = 4$.

Exercise 13 – Temperature conversion

$F = 1.8 \cdot 20 + 32 = 68$.

1.8 is the rate: each 1°C increase raises the temperature 1.8°F.

68°F; 1.8°F per 1°C

Exercise 14 – Gas tank

Gas left.

$g = 14 – 0.04m$.

$g = 14 – 0.04 \cdot 250 = 4$.

$0 = 14 – 0.04m$, so $m = 350$.

4 gallons; empty after 350 miles

Exercise 15 – Qualitative curve

It is nonlinear (a curve). The height increases, reaches a maximum near 2 seconds, then decreases.

Nonlinear; increasing then decreasing

Exercise 16 – Compare two plans

Plans A and B.

Rate A: 15. Rate B: 18.

After 6 months: A $= 15 \cdot 6 + 20 = 110$; B $= 18 \cdot 6 + 10 = 118$.

B has the greater rate; A costs less after 6 months

Exercise 17 – Proportional special case

When $x = 0$, $y = 0$, so the equation is $y = mx$ and the relationship is proportional.

It is proportional

Exercise 18 – Streaming

Rate: $\frac{45 – 27}{5 – 3} = 9$ dollars per month.

$27 = 9 \cdot 3 + b$, so $b = 0$.

\$9 per month; no sign-up fee

Exercise 19 – Meaning of an intercept

Set $L = 0$: $30 = 2d$, so $d = 15$.

(15, 0): the pond is empty after 15 days

Exercise 20 – Piecewise story

0 to 1 hour: walked away at 4 mph. 1 to 3 hours: stayed 4 miles from home. 3 to 4 hours: walked home at 4 mph.

Walk out, stay, walk back

Key facts behind this linear function models answers

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 answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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

All Grade 8 chapters: Grade 8 math.

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